src/bliss/graph.cc

// #include <cstdio>
#include <cassert>
#include <climits>
#include <set>
#include <list>
#include <algorithm>

#include "defs.hh"
#include "graph.hh"
#include "partition.hh"
#include "utils.hh"

/* use 'and' instead of '&&' */
#if _MSC_VER
#include <ciso646>
#endif

/*
  Copyright (c) 2003-2015 Tommi Junttila
  Released under the GNU Lesser General Public License version 3.

  This file is part of bliss.

  bliss is free software: you can redistribute it and/or modify
  it under the terms of the GNU Lesser General Public License as published by
  the Free Software Foundation, version 3 of the License.

  bliss is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General Public License
  along with bliss.  If not, see <http://www.gnu.org/licenses/>.
*/


namespace bliss {

#define _INTERNAL_ERROR() fatal_error("%s:%d: internal error",__FILE__,__LINE__)
#define _OUT_OF_MEMORY() fatal_error("%s:%d: out of memory",__FILE__,__LINE__)

/*-------------------------------------------------------------------------
 *
 * Constructor and destructor routines for the abstract graph class
 *
 *-------------------------------------------------------------------------*/


AbstractGraph::AbstractGraph()
{
  /* Initialize stuff */
  first_path_labeling = 0;
  first_path_labeling_inv = 0;
  best_path_labeling = 0;
  best_path_labeling_inv = 0;
  first_path_automorphism = 0;
  best_path_automorphism = 0;
  in_search = false;
  refine_equal_to_first = false;

  /* Default value for using "long prune" */
  opt_use_long_prune = true;
  /* Default value for using failure recording */
  opt_use_failure_recording = true;
  /* Default value for using component recursion */
  opt_use_comprec = true;


  verbose_level = 0;
  // verbstr = stdout;

  report_hook = 0;
  report_user_param = 0;
}


AbstractGraph::~AbstractGraph()
{
  if(first_path_labeling) {
    free(first_path_labeling); first_path_labeling = 0; }
  if(first_path_labeling_inv) {
    free(first_path_labeling_inv); first_path_labeling_inv = 0; }
  if(best_path_labeling) {
    free(best_path_labeling); best_path_labeling = 0; }
  if(best_path_labeling_inv) {
    free(best_path_labeling_inv); best_path_labeling_inv = 0; }
  if(first_path_automorphism) {
    free(first_path_automorphism); first_path_automorphism = 0; }
  if(best_path_automorphism) {
    free(best_path_automorphism); best_path_automorphism = 0; }

  report_hook = 0;
  report_user_param = 0;
}


/*-------------------------------------------------------------------------
 *
 * Verbose output management routines
 *
 *-------------------------------------------------------------------------*/

void
AbstractGraph::set_verbose_level(const unsigned int level)
{
  verbose_level = level;
}

void
AbstractGraph::set_verbose_file(FILE* const fp)
{
  // verbstr = fp;
}


/*-------------------------------------------------------------------------
 *
 * Routines for refinement to equitable partition
 *
 *-------------------------------------------------------------------------*/

void
AbstractGraph::refine_to_equitable()
{

  /* Start refinement from all cells -> push 'em all in the splitting queue */
  for(Partition::Cell* cell = p.first_cell; cell; cell = cell->next)
    p.splitting_queue_add(cell);

  do_refine_to_equitable();

}

void
AbstractGraph::refine_to_equitable(Partition::Cell* const unit_cell)
{

  p.splitting_queue_add(unit_cell);

  do_refine_to_equitable();
}


void
AbstractGraph::refine_to_equitable(Partition::Cell* const unit_cell1,
				   Partition::Cell* const unit_cell2)
{

  p.splitting_queue_add(unit_cell1);
  p.splitting_queue_add(unit_cell2);

  do_refine_to_equitable();
}


bool
AbstractGraph::do_refine_to_equitable()
{

  eqref_hash.reset();

  while(!p.splitting_queue_is_empty())
    {
      Partition::Cell* const cell = p.splitting_queue_pop();

      if(cell->is_unit())
	{
	  if(in_search) {
	    const unsigned int index = cell->first;
	    if(first_path_automorphism)
	      {
		/* Build the (potential) automorphism on-the-fly */
		first_path_automorphism[first_path_labeling_inv[index]] =
		  p.elements[index];
	      }
	    if(best_path_automorphism)
	      {
		/* Build the (potential) automorphism on-the-fly */
		best_path_automorphism[best_path_labeling_inv[index]] =
		  p.elements[index];
	      }
	  }
	  const bool worse = split_neighbourhood_of_unit_cell(cell);
	  if(in_search and worse)
	    goto worse_exit;
	}
      else
	{
	  const bool worse = split_neighbourhood_of_cell(cell);
	  if(in_search and worse)
	    goto worse_exit;
	}
    }

  return true;

 worse_exit:
  /* Clear splitting_queue */
  p.splitting_queue_clear();
  return false;
}


/*-------------------------------------------------------------------------
 *
 * Routines for handling the canonical labeling
 *
 *-------------------------------------------------------------------------*/

/** \internal
 * Assign the labeling induced by the current partition 'this.p' to
 * \a labeling.
 * That is, if the partition is [[2,0],[1]],
 * then \a labeling will map 0 to 1, 1 to 2, and 2 to 0.
 */
void
AbstractGraph::update_labeling(unsigned int* const labeling)
{
  const unsigned int N = get_nof_vertices();
  unsigned int* ep = p.elements;
  for(unsigned int i = 0; i < N; i++, ep++)
    labeling[*ep] = i;
}

/** \internal
 * The same as update_labeling() except that the inverse of the labeling
 * is also produced and assigned to \a labeling_inv.
 */
void
AbstractGraph::update_labeling_and_its_inverse(unsigned int* const labeling,
					       unsigned int* const labeling_inv)
{
  const unsigned int N = get_nof_vertices();
  unsigned int* ep = p.elements;
  unsigned int* clip = labeling_inv;

  for(unsigned int i = 0; i < N; ) {
    labeling[*ep] = i;
    i++;
    *clip = *ep;
    ep++;
    clip++;
  }
}


/*-------------------------------------------------------------------------
 *
 * Routines for handling automorphisms
 *
 *-------------------------------------------------------------------------*/


/** \internal
 * Reset the permutation \a perm to the identity permutation.
 */
void
AbstractGraph::reset_permutation(unsigned int* perm)
{
  const unsigned int N = get_nof_vertices();
  for(unsigned int i = 0; i < N; i++, perm++)
    *perm = i;
}

bool
AbstractGraph::is_automorphism(unsigned int* const perm)
{
  _INTERNAL_ERROR();
  return false;
}

bool
AbstractGraph::is_automorphism(const std::vector<unsigned int>& perm) const
{
  _INTERNAL_ERROR();
  return false;
}


/*-------------------------------------------------------------------------
 *
 * Certificate building
 *
 *-------------------------------------------------------------------------*/

void
AbstractGraph::cert_add(const unsigned int v1,
			const unsigned int v2,
			const unsigned int v3)
{
  if(refine_compare_certificate)
    {
      if(refine_equal_to_first)
	{
	  /* So far equivalent to the first path... */
	  unsigned int index = certificate_current_path.size();
	  if(index >= refine_first_path_subcertificate_end)
	    {
	      refine_equal_to_first = false;
	    }
	  else if(certificate_first_path[index] != v1)
	    {
	      refine_equal_to_first = false;
	    }
	  else if(certificate_first_path[++index] != v2)
	    {
	      refine_equal_to_first = false;
	    }
	  else if(certificate_first_path[++index] != v3)
	    {
	      refine_equal_to_first = false;
	    }
	  if(opt_use_failure_recording and !refine_equal_to_first)
	    {
	      /* We just became different from the first path,
	       * remember the deviation point tree-specific invariant
	       * for the use of failure recording */
	      UintSeqHash h;
	      h.update(v1);
	      h.update(v2);
	      h.update(v3);
	      h.update(index);
	      h.update(eqref_hash.get_value());
	      failure_recording_fp_deviation = h.get_value();
	    }
	}
      if(refine_cmp_to_best == 0)
	{
	  /* So far equivalent to the current best path... */
	  unsigned int index = certificate_current_path.size();
	  if(index >= refine_best_path_subcertificate_end)
	    {
	      refine_cmp_to_best = 1;
	    }
	  else if(v1 > certificate_best_path[index])
	    {
	      refine_cmp_to_best = 1;
	    }
	  else if(v1 < certificate_best_path[index])
	    {
	      refine_cmp_to_best = -1;
	    }
	  else if(v2 > certificate_best_path[++index])
	    {
	      refine_cmp_to_best = 1;
	    }
	  else if(v2 < certificate_best_path[index])
	    {
	      refine_cmp_to_best = -1;
	    }
	  else if(v3 > certificate_best_path[++index])
	    {
	      refine_cmp_to_best = 1;
	    }
	  else if(v3 < certificate_best_path[index])
	    {
	      refine_cmp_to_best = -1;
	    }
	}
      if((refine_equal_to_first == false) and
	 (refine_cmp_to_best < 0))
	return;
    }
  /* Update the current path certificate */
  certificate_current_path.push_back(v1);
  certificate_current_path.push_back(v2);
  certificate_current_path.push_back(v3);
}


void
AbstractGraph::cert_add_redundant(const unsigned int v1,
				  const unsigned int v2,
				  const unsigned int v3)
{
  return cert_add(v1, v2, v3);
}


/*-------------------------------------------------------------------------
 *
 * Long prune code
 *
 *-------------------------------------------------------------------------*/

void
AbstractGraph::long_prune_init()
{
  const unsigned int N = get_nof_vertices();
  long_prune_temp.clear();
  long_prune_temp.resize(N);
  /* Of how many automorphisms we can store information in
     the predefined, fixed amount of memory? */
  const unsigned int nof_fitting_in_max_mem =
    (long_prune_options_max_mem * 1024 * 1024) / (((N * 2) / 8)+1);
  long_prune_max_stored_autss = long_prune_options_max_stored_auts;
  /* Had some problems with g++ in using (a<b)?a:b when constants involved,
     so had to make this in a stupid way... */
  if(nof_fitting_in_max_mem < long_prune_options_max_stored_auts)
    long_prune_max_stored_autss = nof_fitting_in_max_mem;

  long_prune_deallocate();
  long_prune_fixed.resize(N, 0);
  long_prune_mcrs.resize(N, 0);
  long_prune_begin = 0;
  long_prune_end = 0;
}

void
AbstractGraph::long_prune_deallocate()
{
  while(!long_prune_fixed.empty())
    {
      delete long_prune_fixed.back();
      long_prune_fixed.pop_back();
    }
  while(!long_prune_mcrs.empty())
    {
      delete long_prune_mcrs.back();
      long_prune_mcrs.pop_back();
    }
}

void
AbstractGraph::long_prune_swap(const unsigned int i, const unsigned int j)
{
  const unsigned int real_i = i % long_prune_max_stored_autss;
  const unsigned int real_j = j % long_prune_max_stored_autss;
  std::vector<bool>* tmp = long_prune_fixed[real_i];
  long_prune_fixed[real_i] = long_prune_fixed[real_j];
  long_prune_fixed[real_j] = tmp;
  tmp = long_prune_mcrs[real_i];
  long_prune_mcrs[real_i] = long_prune_mcrs[real_j];
  long_prune_mcrs[real_j] = tmp;
}

std::vector<bool>&
AbstractGraph::long_prune_allocget_fixed(const unsigned int index)
{
  const unsigned int i = index % long_prune_max_stored_autss;
  if(!long_prune_fixed[i])
    long_prune_fixed[i] = new std::vector<bool>(get_nof_vertices());
  return *long_prune_fixed[i];
}

std::vector<bool>&
AbstractGraph::long_prune_get_fixed(const unsigned int index)
{
  return *long_prune_fixed[index % long_prune_max_stored_autss];
}

std::vector<bool>&
AbstractGraph::long_prune_allocget_mcrs(const unsigned int index)
{
  const unsigned int i = index % long_prune_max_stored_autss;
  if(!long_prune_mcrs[i])
    long_prune_mcrs[i] = new std::vector<bool>(get_nof_vertices());
  return *long_prune_mcrs[i];
}

std::vector<bool>&
AbstractGraph::long_prune_get_mcrs(const unsigned int index)
{
  return *long_prune_mcrs[index % long_prune_max_stored_autss];
}

void
AbstractGraph::long_prune_add_automorphism(const unsigned int* aut)
{
  if(long_prune_max_stored_autss == 0)
    return;

  const unsigned int N = get_nof_vertices();


  /* If the buffer of stored auts is full, remove the oldest aut */
  if(long_prune_end - long_prune_begin == long_prune_max_stored_autss)
    {
      long_prune_begin++;
    }
  long_prune_end++;
  std::vector<bool>& fixed = long_prune_allocget_fixed(long_prune_end-1);
  std::vector<bool>& mcrs = long_prune_allocget_mcrs(long_prune_end-1);
  /* Mark nodes that are (i) fixed or (ii) minimal orbit representatives
   * under the automorphism 'aut' */
  for(unsigned int i = 0; i < N; i++)
    {
      fixed[i] = (aut[i] == i);
      if(long_prune_temp[i] == false)
	{
	  mcrs[i] = true;
	  unsigned int j = aut[i];
	  while(j != i)
	    {
	      long_prune_temp[j] = true;
	      j = aut[j];
	    }
	}
      else
	{
	  mcrs[i] = false;
	}
      /* Clear the temp array on-the-fly... */
      long_prune_temp[i] = false;
    }


}


/*-------------------------------------------------------------------------
 *
 * Routines for handling orbit information
 *
 *-------------------------------------------------------------------------*/

void
AbstractGraph::update_orbit_information(Orbit& o, const unsigned int* perm)
{
  const unsigned int N = get_nof_vertices();
  for(unsigned int i = 0; i < N; i++)
    if(perm[i] != i)
      o.merge_orbits(i, perm[i]);
}


/*-------------------------------------------------------------------------
 *
 * The actual backtracking search
 *
 *-------------------------------------------------------------------------*/

class TreeNode
{
  //friend class AbstractGraph;
public:
  unsigned int split_cell_first;

  int split_element;
  static const int SPLIT_START = -1;
  static const int SPLIT_END   = -2;

  Partition::BacktrackPoint partition_bt_point;

  unsigned int certificate_index;

  static const char NO = -1;
  static const char MAYBE = 0;
  static const char YES = 1;

  /* First path stuff */
  bool fp_on;
  bool fp_cert_equal;
  char fp_extendable;

  /* Best path stuff */
  bool in_best_path;
  int cmp_to_best_path;

  unsigned int failure_recording_ival;

  /* Component recursion related data */
  unsigned int cr_cep_stack_size;
  unsigned int cr_cep_index;
  unsigned int cr_level;

  bool needs_long_prune;
  unsigned int long_prune_begin;
  std::set<unsigned int, std::less<unsigned int> > long_prune_redundant;

  UintSeqHash eqref_hash;
  unsigned int subcertificate_length;
};


typedef struct {
  unsigned int splitting_element;
  unsigned int certificate_index;
  unsigned int subcertificate_length;
  UintSeqHash eqref_hash;
} PathInfo;


void
AbstractGraph::search(const bool canonical, Stats& stats)
{
  const unsigned int N = get_nof_vertices();

  unsigned int all_same_level = UINT_MAX;

  p.graph = this;

  /*
   * Must be done!
   */
  remove_duplicate_edges();

  /*
   * Reset search statistics
   */
  stats.reset();
  stats.nof_nodes = 1;
  stats.nof_leaf_nodes = 1;

  /* Free old first path data structures */
  if(first_path_labeling) {
    free(first_path_labeling); first_path_labeling = 0; }
  if(first_path_labeling_inv) {
    free(first_path_labeling_inv); first_path_labeling_inv = 0; }
  if(first_path_automorphism) {
    free(first_path_automorphism); first_path_automorphism = 0; }

  /* Free old best path data structures */
  if(best_path_labeling) {
    free(best_path_labeling); best_path_labeling = 0; }
  if(best_path_labeling_inv) {
    free(best_path_labeling_inv); best_path_labeling_inv = 0; }
  if(best_path_automorphism) {
    free(best_path_automorphism); best_path_automorphism = 0; }

  if(N == 0)
    {
      /* Nothing to do, return... */
      return;
    }

  /* Initialize the partition ... */
  p.init(N);
  /* ... and the component recursion data structures in the partition */
  if(opt_use_comprec)
    p.cr_init();

  neighbour_heap.init(N);

  in_search = false;
  /* Do not compute certificate when building the initial partition */
  refine_compare_certificate = false;
  /* The 'eqref_hash' hash value is not computed when building
   * the initial partition as it is not used for anything at the moment.
   * This saves some cycles. */
  compute_eqref_hash = false;

  make_initial_equitable_partition();

  /*
   * Allocate space for the "first path" and "best path" labelings
   */
  if(first_path_labeling) free(first_path_labeling);
  first_path_labeling = (unsigned int*)calloc(N, sizeof(unsigned int));
  if(!first_path_labeling) _OUT_OF_MEMORY();
  if(best_path_labeling) free(best_path_labeling);
  best_path_labeling = (unsigned int*)calloc(N, sizeof(unsigned int));
  if(!best_path_labeling) _OUT_OF_MEMORY();

  /*
   * Is the initial partition discrete?
   */
  if(p.is_discrete())
    {
      /* Make the best path labeling i.e. the canonical labeling */
      update_labeling(best_path_labeling);
      /* Update statistics */
      stats.nof_leaf_nodes = 1;
      /* Free component recursion data */
      if(opt_use_comprec)
        p.cr_free();
      return;
    }

  /*
   * Allocate the inverses of the "first path" and "best path" labelings
   */
  if(first_path_labeling_inv) free(first_path_labeling_inv);
  first_path_labeling_inv = (unsigned int*)calloc(N, sizeof(unsigned int));
  if(!first_path_labeling_inv) _OUT_OF_MEMORY();
  if(best_path_labeling_inv) free(best_path_labeling_inv);
  best_path_labeling_inv = (unsigned int*)calloc(N, sizeof(unsigned int));
  if(!best_path_labeling_inv) _OUT_OF_MEMORY();

  /*
   * Allocate space for the automorphisms
   */
  if(first_path_automorphism) free(first_path_automorphism);
  first_path_automorphism = (unsigned int*)malloc(N * sizeof(unsigned int));
  if(!first_path_automorphism) _OUT_OF_MEMORY();
  if(best_path_automorphism) free(best_path_automorphism);
  best_path_automorphism = (unsigned int*)malloc(N * sizeof(unsigned int));
  if(!best_path_automorphism) _OUT_OF_MEMORY();

  /*
   * Initialize orbit information so that all vertices are in their own orbits
   */
  first_path_orbits.init(N);
  best_path_orbits.init(N);

  /*
   * Initialize certificate memory
   */
  initialize_certificate();

  std::vector<TreeNode> search_stack;
  std::vector<PathInfo> first_path_info;
  std::vector<PathInfo> best_path_info;

  search_stack.clear();

  /* Initialize "long prune" data structures */
  if(opt_use_long_prune)
    long_prune_init();

  /*
   * Initialize failure recording data structures
   */
  typedef std::set<unsigned int, std::less<unsigned int> > FailureRecordingSet;
  std::vector<FailureRecordingSet> failure_recording_hashes;

  /*
   * Initialize component recursion data structures
   */
  cr_cep_stack.clear();
  unsigned int cr_cep_index = 0;
  {
    /* Inset a sentinel "component end point" */
    CR_CEP sentinel;
    sentinel.creation_level = 0;
    sentinel.discrete_cell_limit = get_nof_vertices();
    sentinel.next_cr_level = 0;
    sentinel.next_cep_index = 0;
    sentinel.first_checked = false;
    sentinel.best_checked = false;
    cr_cep_index = 0;
    cr_cep_stack.push_back(sentinel);
  }
  cr_level = 0;
  if(opt_use_comprec and
     nucr_find_first_component(cr_level) == true and
     p.nof_discrete_cells() + cr_component_elements <
     cr_cep_stack[cr_cep_index].discrete_cell_limit)
    {
      cr_level = p.cr_split_level(0, cr_component);
      CR_CEP cep;
      cep.creation_level = 0;
      cep.discrete_cell_limit = p.nof_discrete_cells() + cr_component_elements;
      cep.next_cr_level = 0;
      cep.next_cep_index = cr_cep_index;
      cep.first_checked = false;
      cep.best_checked = false;
      cr_cep_index = cr_cep_stack.size();
      cr_cep_stack.push_back(cep);
    }

  /*
   * Build the root node of the search tree
   */
  {
    TreeNode root;
    Partition::Cell* split_cell = find_next_cell_to_be_splitted(p.first_cell);
    root.split_cell_first = split_cell->first;
    root.split_element = TreeNode::SPLIT_START;
    root.partition_bt_point = p.set_backtrack_point();
    root.certificate_index = 0;
    root.fp_on = true;
    root.fp_cert_equal = true;
    root.fp_extendable = TreeNode::MAYBE;
    root.in_best_path = false;
    root.cmp_to_best_path = 0;
    root.long_prune_begin = 0;
    root.needs_long_prune = false;

    root.failure_recording_ival = 0;

    /* Save component recursion info for backtracking */
    root.cr_level = cr_level;
    root.cr_cep_stack_size = cr_cep_stack.size();
    root.cr_cep_index = cr_cep_index;
    search_stack.push_back(root);
  }

  /*
   * Set status and global flags for search related procedures
   */
  in_search = true;
  /* Do not compare certificates during refinement until the first path has been traversed to the leaf */
  refine_compare_certificate = false;


  /*
   * The actual backtracking search
   */
  while(!search_stack.empty())
    {
      TreeNode&          current_node  = search_stack.back();
      const unsigned int current_level = (unsigned int)search_stack.size()-1;


      if(opt_use_comprec)
	{
	  CR_CEP& cep = cr_cep_stack[current_node.cr_cep_index];
	  if(cep.first_checked == true and
	     current_node.fp_extendable == TreeNode::MAYBE and
	     !search_stack[cep.creation_level].fp_on)
	    {
	      current_node.fp_extendable = TreeNode::NO;
	    }
	}

      if(current_node.fp_on)
	{
	  if(current_node.split_element == TreeNode::SPLIT_END)
	    {
	      search_stack.pop_back();
	      continue;
	    }
	}
      else
	{
	  if(current_node.fp_extendable == TreeNode::YES)
	    {
	      search_stack.pop_back();
	      continue;
	    }
	  if(current_node.split_element == TreeNode::SPLIT_END)
	    {
	      if(opt_use_failure_recording)
		{
		  TreeNode& parent_node = search_stack[current_level-1];
		  if(parent_node.fp_on)
		    failure_recording_hashes[current_level-1].insert(current_node.failure_recording_ival);
		}
	      search_stack.pop_back();
	      continue;
	    }
	  if(current_node.fp_extendable == TreeNode::NO and
	     (!canonical or current_node.cmp_to_best_path < 0))
	    {
	      if(opt_use_failure_recording)
		{
		  TreeNode& parent_node = search_stack[current_level-1];
		  if(parent_node.fp_on)
		    failure_recording_hashes[current_level-1].insert(current_node.failure_recording_ival);
		}
	      search_stack.pop_back();
	      continue;
	    }
	}

      /* Restore partition ... */
      p.goto_backtrack_point(current_node.partition_bt_point);
      /* ... and re-remember backtracking point */
      current_node.partition_bt_point = p.set_backtrack_point();

      /* Restore current path certificate */
      certificate_index = current_node.certificate_index;
      refine_current_path_certificate_index = current_node.certificate_index;
      certificate_current_path.resize(certificate_index);

      /* Fetch split cell information */
      Partition::Cell * const cell =
	p.get_cell(p.elements[current_node.split_cell_first]);

      /* Restore component recursion information */
      cr_level = current_node.cr_level;
      cr_cep_stack.resize(current_node.cr_cep_stack_size);
      cr_cep_index = current_node.cr_cep_index;


      /*
       * Update long prune redundancy sets
       */
      if(opt_use_long_prune and current_level >= 1 and !current_node.fp_on)
	{
	  unsigned int begin = (current_node.long_prune_begin>long_prune_begin)?current_node.long_prune_begin:long_prune_begin;
	  for(unsigned int i = begin; i < long_prune_end; i++)
	    {
	      const std::vector<bool>& fixed = long_prune_get_fixed(i);
#if defined(BLISS_CONSISTENCY_CHECKS)
	      for(unsigned int l = 0; l < search_stack.size()-2; l++)
		assert(fixed[search_stack[l].split_element]);
#endif
	      if(fixed[search_stack[search_stack.size()-1-1].split_element] ==
		 false)
		{
		  long_prune_swap(begin, i);
		  begin++;
		  current_node.long_prune_begin = begin;
		  continue;
		}
	    }

	  if(current_node.split_element == TreeNode::SPLIT_START)
	    {
	      current_node.needs_long_prune = true;
	    }
	  else if(current_node.needs_long_prune)
	    {
	      current_node.needs_long_prune = false;
	      unsigned int begin = (current_node.long_prune_begin>long_prune_begin)?current_node.long_prune_begin:long_prune_begin;
	      for(unsigned int i = begin; i < long_prune_end; i++)
		{
		  const std::vector<bool>& fixed = long_prune_get_fixed(i);
#if defined(BLISS_CONSISTENCY_CHECKS)
		  for(unsigned int l = 0; l < search_stack.size()-2; l++)
		    assert(fixed[search_stack[l].split_element]);
#endif
		  assert(fixed[search_stack[current_level-1].split_element] == true);
		  if(fixed[search_stack[current_level-1].split_element] == false)
		    {
		      long_prune_swap(begin, i);
		      begin++;
		      current_node.long_prune_begin = begin;
		      continue;
		    }
		  const std::vector<bool>& mcrs = long_prune_get_mcrs(i);
		  unsigned int* ep = p.elements + cell->first;
		  for(unsigned int j = cell->length; j > 0; j--, ep++) {
		    if(mcrs[*ep] == false)
		      current_node.long_prune_redundant.insert(*ep);
		  }
		}
	    }
	}


      /*
       * Find the next smallest, non-isomorphic element in the cell and
       * store it in current_node.split_element
       */
      {
	unsigned int  next_split_element = UINT_MAX;
	//unsigned int* next_split_element_pos = 0;
	unsigned int* ep = p.elements + cell->first;
	if(current_node.fp_on)
	  {
	    /* Find the next larger splitting element that is
	     * a minimal orbit representative w.r.t. first_path_orbits */
	    for(unsigned int i = cell->length; i > 0; i--, ep++) {
	      if((int)(*ep) > current_node.split_element and
		 *ep < next_split_element and
		 first_path_orbits.is_minimal_representative(*ep)) {
		next_split_element = *ep;
		//next_split_element_pos = ep;
	      }
	    }
	  }
	else if(current_node.in_best_path)
	  {
	    /* Find the next larger splitting element that is
	     * a minimal orbit representative w.r.t. best_path_orbits */
	    for(unsigned int i = cell->length; i > 0; i--, ep++) {
	      if((int)(*ep) > current_node.split_element and
		 *ep < next_split_element and
		 best_path_orbits.is_minimal_representative(*ep) and
		 (!opt_use_long_prune or
		  current_node.long_prune_redundant.find(*ep) ==
		  current_node.long_prune_redundant.end())) {
		next_split_element = *ep;
		//next_split_element_pos = ep;
	      }
	    }
	  }
	else
	  {
	    /* Find the next larger splitting element */
	    for(unsigned int i = cell->length; i > 0; i--, ep++) {
	      if((int)(*ep) > current_node.split_element and
		 *ep < next_split_element and
		 (!opt_use_long_prune or
		  current_node.long_prune_redundant.find(*ep) ==
		  current_node.long_prune_redundant.end())) {
		next_split_element = *ep;
		//next_split_element_pos = ep;
	      }
	    }
	  }
	if(next_split_element == UINT_MAX)
	  {
	    /* No more (unexplored children) in the cell */
	    current_node.split_element = TreeNode::SPLIT_END;
	    if(current_node.fp_on)
	      {
		/* Update group size */
		const unsigned int index = first_path_orbits.orbit_size(first_path_info[search_stack.size()-1].splitting_element);
		stats.group_size.multiply(index);
		stats.group_size_approx *= (long double)index;
		/*
		 * Update all_same_level
		 */
		if(index == cell->length and all_same_level == current_level+1)
		  all_same_level = current_level;
	      }
	    continue;
	  }

	/* Split on smallest */
	current_node.split_element = next_split_element;
      }

      const unsigned int child_level = current_level+1;
      /* Update some statistics */
      stats.nof_nodes++;
      if(search_stack.size() > stats.max_level)
	stats.max_level = search_stack.size();


      /* Set flags and indices for the refiner certificate builder */
      refine_equal_to_first = current_node.fp_cert_equal;
      refine_cmp_to_best = current_node.cmp_to_best_path;
      if(!first_path_info.empty())
	{
	  if(refine_equal_to_first)
	    refine_first_path_subcertificate_end =
	      first_path_info[search_stack.size()-1].certificate_index +
	      first_path_info[search_stack.size()-1].subcertificate_length;
	  if(canonical)
	    {
	      if(refine_cmp_to_best == 0)
		refine_best_path_subcertificate_end =
		  best_path_info[search_stack.size()-1].certificate_index +
		  best_path_info[search_stack.size()-1].subcertificate_length;
	    }
	  else
	    refine_cmp_to_best = -1;
	}

      const bool was_fp_cert_equal = current_node.fp_cert_equal;

      /* Individualize, i.e. split the cell in two, the latter new cell
       * will be a unit one containing info.split_element */
      Partition::Cell* const new_cell =
	p.individualize(cell, current_node.split_element);

      /*
       * Refine the new partition to equitable
       */
      if(cell->is_unit())
	refine_to_equitable(cell, new_cell);
      else
	refine_to_equitable(new_cell);


      /* Update statistics */
      if(p.is_discrete())
	stats.nof_leaf_nodes++;


      if(!first_path_info.empty())
	{
	  /* We are no longer on the first path */
	  const unsigned int subcertificate_length =
	    certificate_current_path.size() - certificate_index;
	  if(refine_equal_to_first)
	    {
	      /* Was equal to the first path so far */
	      PathInfo& first_pinfo = first_path_info[current_level];
	      assert(first_pinfo.certificate_index == certificate_index);
	      if(subcertificate_length != first_pinfo.subcertificate_length)
		{
		  refine_equal_to_first = false;
		  if(opt_use_failure_recording)
		    failure_recording_fp_deviation = subcertificate_length;
		}
	      else if(first_pinfo.eqref_hash.cmp(eqref_hash) != 0)
		{
		  refine_equal_to_first = false;
		  if(opt_use_failure_recording)
		    failure_recording_fp_deviation = eqref_hash.get_value();
		}
	    }
	  if(canonical and (refine_cmp_to_best == 0))
	    {
	      /* Was equal to the best path so far */
	      PathInfo& bestp_info = best_path_info[current_level];
	      assert(bestp_info.certificate_index == certificate_index);
	      if(subcertificate_length < bestp_info.subcertificate_length)
		{
		  refine_cmp_to_best = -1;
		}
	      else if(subcertificate_length > bestp_info.subcertificate_length)
		{
		  refine_cmp_to_best = 1;
		}
	      else if(bestp_info.eqref_hash.cmp(eqref_hash) > 0)
		{
		  refine_cmp_to_best = -1;
		}
	      else if(bestp_info.eqref_hash.cmp(eqref_hash) < 0)
		{
		  refine_cmp_to_best = 1;
		}
	    }

	  if(opt_use_failure_recording and
	     was_fp_cert_equal and
	     !refine_equal_to_first)
	    {
	      UintSeqHash k;
	      k.update(failure_recording_fp_deviation);
	      k.update(eqref_hash.get_value());
	      failure_recording_fp_deviation = k.get_value();

	      if(current_node.fp_on)
		failure_recording_hashes[current_level].insert(failure_recording_fp_deviation);
	      else
		{
		  for(unsigned int i = current_level; i > 0; i--)
		    {
		      if(search_stack[i].fp_on)
			break;
		      const FailureRecordingSet& s = failure_recording_hashes[i];
		      if(i == current_level and
			 s.find(failure_recording_fp_deviation) != s.end())
			break;
		      if(s.find(0) != s.end())
			break;
		      search_stack[i].fp_extendable = TreeNode::NO;
		    }
		}
	    }


	  /* Check if no longer equal to the first path and,
	   * if canonical labeling is desired, also worse than the
	   * current best path */
	  if(refine_equal_to_first == false and
	     (!canonical or (refine_cmp_to_best < 0)))
	    {
	      /* Yes, backtrack */
	      stats.nof_bad_nodes++;
	      if(current_node.fp_cert_equal == true and
		 current_level+1 > all_same_level)
		{
		  assert(all_same_level >= 1);
		  for(unsigned int i = all_same_level;
		      i < search_stack.size();
		      i++)
		    {
		      search_stack[i].fp_extendable = TreeNode::NO;
		    }
		}

	      continue;
	    }
	}

#if defined(BLISS_VERIFY_EQUITABLEDNESS)
      /* The new partition should be equitable */
      if(!is_equitable())
	fatal_error("consistency check failed - partition after refinement is not equitable");
#endif

      /*
       * Next level search tree node info
       */
      TreeNode child_node;

      /* No more in the first path */
      child_node.fp_on = false;
      /* No more in the best path */
      child_node.in_best_path = false;

      child_node.fp_cert_equal = refine_equal_to_first;
      if(current_node.fp_extendable == TreeNode::NO or
	 (current_node.fp_extendable == TreeNode::MAYBE and
	  child_node.fp_cert_equal == false))
	child_node.fp_extendable = TreeNode::NO;
      else
	child_node.fp_extendable = TreeNode::MAYBE;
      child_node.cmp_to_best_path = refine_cmp_to_best;

      child_node.failure_recording_ival = 0;
      child_node.cr_cep_stack_size = current_node.cr_cep_stack_size;
      child_node.cr_cep_index = current_node.cr_cep_index;
      child_node.cr_level = current_node.cr_level;

      certificate_index = certificate_current_path.size();

      current_node.eqref_hash = eqref_hash;
      current_node.subcertificate_length =
	certificate_index - current_node.certificate_index;


      /*
       * The first encountered leaf node at the end of the "first path"?
       */
      if(p.is_discrete() and first_path_info.empty())
	{
	  //fprintf(stdout, "Level %u: FIRST\n", child_level); fflush(stdout);
	  stats.nof_canupdates++;
	  /*
	   * Update labelings and their inverses
	   */
	  update_labeling_and_its_inverse(first_path_labeling,
					  first_path_labeling_inv);
	  update_labeling_and_its_inverse(best_path_labeling,
					  best_path_labeling_inv);
	  /*
	   * Reset automorphism array
	   */
	  reset_permutation(first_path_automorphism);
	  reset_permutation(best_path_automorphism);
	  /*
	   * Reset orbit information
	   */
	  first_path_orbits.reset();
	  best_path_orbits.reset();
	  /*
	   * Reset group size
	   */
	  stats.group_size.assign(1);
	  stats.group_size_approx = 1.0;
	  /*
	   * Reset all_same_level
	   */
	  all_same_level = child_level;
	  /*
	   * Mark the current path to be the first and best one and save it
	   */
	  const unsigned int base_size = search_stack.size();
	  best_path_info.clear();
	  //fprintf(stdout, " New base is: ");
	  for(unsigned int i = 0; i < base_size; i++) {
	    search_stack[i].fp_on = true;
	    search_stack[i].fp_cert_equal = true;
	    search_stack[i].fp_extendable = TreeNode::YES;
	    search_stack[i].in_best_path = true;
	    search_stack[i].cmp_to_best_path = 0;
	    PathInfo path_info;
	    path_info.splitting_element = search_stack[i].split_element;
	    path_info.certificate_index = search_stack[i].certificate_index;
	    path_info.eqref_hash = search_stack[i].eqref_hash;
	    path_info.subcertificate_length = search_stack[i].subcertificate_length;
	    first_path_info.push_back(path_info);
	    best_path_info.push_back(path_info);
	    //fprintf(stdout, "%u ", search_stack[i].split_element);
	  }
	  //fprintf(stdout, "\n"); fflush(stdout);
	  /* Copy certificates */
	  certificate_first_path = certificate_current_path;
	  certificate_best_path = certificate_current_path;

	  /* From now on, compare certificates when refining */
	  refine_compare_certificate = true;

	  if(opt_use_failure_recording)
	    failure_recording_hashes.resize(base_size);

	  /*
	  for(unsigned int j = 0; j < search_stack.size(); j++)
	    fprintf(stderr, "%u ", search_stack[j].split_element);
	  fprintf(stderr, "\n");
	  p.print(stderr); fprintf(stderr, "\n");
	  */

	  /*
	   * Backtrack to the previous level
	   */
	  continue;
	}


      if(p.is_discrete() and child_node.fp_cert_equal)
	{
	  /*
	   * A leaf node that is equal to the first one.
	   * An automorphism found: aut[i] = elements[first_path_labeling[i]]
	   */
	  goto handle_first_path_automorphism;
	}


      if(!p.is_discrete())
	{
	  Partition::Cell* next_split_cell = 0;
	  /*
	   * An internal, non-leaf node
	   */
	  if(opt_use_comprec)
	    {
	      assert(p.nof_discrete_cells() <=
		     cr_cep_stack[cr_cep_index].discrete_cell_limit);
	      assert(cr_level == child_node.cr_level);


	      if(p.nof_discrete_cells() ==
		 cr_cep_stack[cr_cep_index].discrete_cell_limit)
		{
		  /* We have reached the end of a component */
		  assert(cr_cep_index != 0);
		  CR_CEP& cep = cr_cep_stack[cr_cep_index];

		  /* First, compare with respect to the first path */
		  if(first_path_info.empty() or child_node.fp_cert_equal) {
		    if(cep.first_checked == false)
		      {
			/* First time, go to the next component */
			cep.first_checked = true;
		      }
		    else
		      {
			assert(!first_path_info.empty());
			assert(cep.creation_level < search_stack.size());
			TreeNode& old_info = search_stack[cep.creation_level];
			/* If the component was found when on the first path,
			 * handle the found automorphism as the other
			 * first path automorphisms */
			if(old_info.fp_on)
			  goto handle_first_path_automorphism;
		      }
		  }

		  if(canonical and
		     !first_path_info.empty() and
		     child_node.cmp_to_best_path >= 0) {
		    if(cep.best_checked == false)
		      {
			/* First time, go to the next component */
			cep.best_checked = true;
		      }
		    else
		      {
			assert(cep.creation_level < search_stack.size());
			TreeNode& old_info = search_stack[cep.creation_level];
			if(child_node.cmp_to_best_path == 0) {
			  /* If the component was found when on the best path,
			   * handle the found automorphism as the other
			   * best path automorphisms */
			  if(old_info.in_best_path)
			    goto handle_best_path_automorphism;
			  /* Otherwise, we do not remember the automorhism as
			   * we didn't memorize the path that was invariant
			   * equal to the best one and passed through the
			   * component.
			   * Thus we can only backtrack to the previous level */
			  child_node.cmp_to_best_path = -1;
			  if(!child_node.fp_cert_equal)
			    {
			      continue;
			    }
			}
			else {
			  assert(child_node.cmp_to_best_path > 0);
			  if(old_info.in_best_path)
			    {
			      stats.nof_canupdates++;
			      /*
			       * Update canonical labeling and its inverse
			       */
			      for(unsigned int i = 0; i < N; i++) {
				if(p.get_cell(p.elements[i])->is_unit()) {
				  best_path_labeling[p.elements[i]] = i;
				  best_path_labeling_inv[i] = p.elements[i];
				}
			      }
			      //update_labeling_and_its_inverse(best_path_labeling, best_path_labeling_inv);
			      /* Reset best path automorphism */
			      reset_permutation(best_path_automorphism);
			      /* Reset best path orbit structure */
			      best_path_orbits.reset();
			      /* Mark to be the best one and save prefix */
			      unsigned int postfix_start = cep.creation_level;
			      assert(postfix_start < best_path_info.size());
			      while(p.get_cell(best_path_info[postfix_start].splitting_element)->is_unit()) {
				postfix_start++;
				assert(postfix_start < best_path_info.size());
			      }
			      unsigned int postfix_start_cert = best_path_info[postfix_start].certificate_index;
			      std::vector<PathInfo> best_path_temp = best_path_info;
			      best_path_info.clear();
			      for(unsigned int i = 0; i < search_stack.size(); i++) {
				TreeNode& ss_info = search_stack[i];
				PathInfo  bp_info;
				ss_info.cmp_to_best_path = 0;
				ss_info.in_best_path = true;
				bp_info.splitting_element = ss_info.split_element;
				bp_info.certificate_index = ss_info.certificate_index;
				bp_info.subcertificate_length = ss_info.subcertificate_length;
				bp_info.eqref_hash = ss_info.eqref_hash;
				best_path_info.push_back(bp_info);
			      }
			      /* Copy the postfix of the previous best path */
			      for(unsigned int i = postfix_start;
				  i < best_path_temp.size();
				  i++)
				{
				  best_path_info.push_back(best_path_temp[i]);
				  best_path_info[best_path_info.size()-1].certificate_index =
				    best_path_info[best_path_info.size()-2].certificate_index +
				    best_path_info[best_path_info.size()-2].subcertificate_length;
				}
			      std::vector<unsigned int> certificate_best_path_old = certificate_best_path;
			      certificate_best_path = certificate_current_path;
			      for(unsigned int i = postfix_start_cert;  i < certificate_best_path_old.size(); i++)
				certificate_best_path.push_back(certificate_best_path_old[i]);
			      assert(certificate_best_path.size() == best_path_info.back().certificate_index + best_path_info.back().subcertificate_length);
			      /* Backtrack to the previous level */
			      continue;
			    }
			}
		      }
		  }

		  /* No backtracking performed, go to next componenet */
		  cr_level = cep.next_cr_level;
		  cr_cep_index = cep.next_cep_index;
		}

	      /* Check if the current component has been split into
	       * new non-uniformity subcomponents */
	      //if(nucr_find_first_component(cr_level) == true and
	      // p.nof_discrete_cells() + cr_component_elements <
	      // cr_cep_stack[cr_cep_index].discrete_cell_limit)
	      if(nucr_find_first_component(cr_level, cr_component,
					   cr_component_elements,
					   next_split_cell) == true and
		 p.nof_discrete_cells() + cr_component_elements <
		 cr_cep_stack[cr_cep_index].discrete_cell_limit)
		{
		  const unsigned int next_cr_level =
		    p.cr_split_level(cr_level, cr_component);
		  CR_CEP cep;
		  cep.creation_level = search_stack.size();
		  cep.discrete_cell_limit =
		    p.nof_discrete_cells() + cr_component_elements;
		  cep.next_cr_level = cr_level;
		  cep.next_cep_index = cr_cep_index;
		  cep.first_checked = false;
		  cep.best_checked = false;
		  cr_cep_index = cr_cep_stack.size();
		  cr_cep_stack.push_back(cep);
		  cr_level = next_cr_level;
		}
	    }


	  /*
	   * Build the next node info
	   */
	  /* Find the next cell to be splitted */
	  if(!next_split_cell)
	    next_split_cell = find_next_cell_to_be_splitted(p.get_cell(p.elements[current_node.split_cell_first]));
	  //Partition::Cell * const next_split_cell = find_next_cell_to_be_splitted(p.get_cell(p.elements[current_node.split_cell_first]));
	  child_node.split_cell_first = next_split_cell->first;
	  child_node.split_element = TreeNode::SPLIT_START;
	  child_node.certificate_index = certificate_index;
	  child_node.partition_bt_point = p.set_backtrack_point();
	  child_node.long_prune_redundant.clear();
	  child_node.long_prune_begin = current_node.long_prune_begin;

	  /* Save component recursion info for backtracking */
	  child_node.cr_level = cr_level;
	  child_node.cr_cep_stack_size = cr_cep_stack.size();
	  child_node.cr_cep_index = cr_cep_index;

	  /* Initialize needs_long_prune to prevent a gcc-ubsan warning */
	  child_node.needs_long_prune = true;

	  search_stack.push_back(child_node);
	  continue;
	}

      /*
       * A leaf node not in the first path or equivalent to the first path
       */


      if(child_node.cmp_to_best_path > 0)
	{
	  /*
	   * A new, better representative found
	   */
	  //fprintf(stdout, "Level %u: NEW BEST\n", child_level); fflush(stdout);
	  stats.nof_canupdates++;
	  /*
	   * Update canonical labeling and its inverse
	   */
	  update_labeling_and_its_inverse(best_path_labeling,
					  best_path_labeling_inv);
	  /* Reset best path automorphism */
	  reset_permutation(best_path_automorphism);
	  /* Reset best path orbit structure */
	  best_path_orbits.reset();
	  /*
	   * Mark the current path to be the best one and save it
	   */
	  const unsigned int base_size = search_stack.size();
	  assert(current_level+1 == base_size);
	  best_path_info.clear();
	  for(unsigned int i = 0; i < base_size; i++) {
	    search_stack[i].cmp_to_best_path = 0;
	    search_stack[i].in_best_path = true;
	    PathInfo path_info;
	    path_info.splitting_element = search_stack[i].split_element;
	    path_info.certificate_index = search_stack[i].certificate_index;
	    path_info.subcertificate_length = search_stack[i].subcertificate_length;
	    path_info.eqref_hash = search_stack[i].eqref_hash;
	    best_path_info.push_back(path_info);
	  }
	  certificate_best_path = certificate_current_path;
	  /*
	   * Backtrack to the previous level
	   */
	  continue;
	}


    handle_best_path_automorphism:
      /*
       *
       * Best path automorphism handling
       *
       */
      {

	/*
	 * Equal to the previous best path
	 */
	if(p.is_discrete())
	  {
#if defined(BLISS_CONSISTENCY_CHECKS)
	    /* Verify that the automorphism is correctly built */
	    for(unsigned int i = 0; i < N; i++)
	      assert(best_path_automorphism[i] ==
		     p.elements[best_path_labeling[i]]);
#endif
	  }
	else
	  {
	    /* An automorphism that was found before the partition was discrete.
	     * Set the image of all elements in non-disrete cells accordingly */
	    for(Partition::Cell* c = p.first_nonsingleton_cell; c;
		c = c->next_nonsingleton) {
	      for(unsigned int i = c->first; i < c->first+c->length; i++)
		if(p.get_cell(p.elements[best_path_labeling[p.elements[i]]])->is_unit())
		  best_path_automorphism[p.elements[best_path_labeling[p.elements[i]]]] = p.elements[i];
		else
		  best_path_automorphism[p.elements[i]] = p.elements[i];
	    }
	  }

#if defined(BLISS_VERIFY_AUTOMORPHISMS)
	/* Verify that it really is an automorphism */
	if(!is_automorphism(best_path_automorphism))
	  fatal_error("Best path automorhism validation check failed");
#endif

	unsigned int gca_level_with_first = 0;
	for(unsigned int i = search_stack.size(); i > 0; i--) {
	  if((int)first_path_info[gca_level_with_first].splitting_element !=
	     search_stack[gca_level_with_first].split_element)
	    break;
	  gca_level_with_first++;
	}

	unsigned int gca_level_with_best = 0;
	for(unsigned int i = search_stack.size(); i > 0; i--) {
	  if((int)best_path_info[gca_level_with_best].splitting_element !=
	     search_stack[gca_level_with_best].split_element)
	    break;
	  gca_level_with_best++;
	}

	if(opt_use_long_prune)
	  {
	    /* Record automorphism */
	    long_prune_add_automorphism(best_path_automorphism);
	  }

	/*
	 * Update orbit information
	 */
	update_orbit_information(best_path_orbits, best_path_automorphism);

	/*
	 * Update orbit information
	 */
	const unsigned int nof_old_orbits = first_path_orbits.nof_orbits();
	update_orbit_information(first_path_orbits, best_path_automorphism);
	if(nof_old_orbits != first_path_orbits.nof_orbits())
	  {
	    /* Some orbits were merged */
	    /* Report automorphism */
	    if(report_hook)
	      (*report_hook)(report_user_param,
			     get_nof_vertices(),
			     best_path_automorphism);
	    /* Update statistics */
	    stats.nof_generators++;
	  }

	/*
	 * Compute backjumping level
	 */
	unsigned int backjumping_level = current_level+1-1;
	if(!first_path_orbits.is_minimal_representative(search_stack[gca_level_with_first].split_element))
	  {
	    backjumping_level = gca_level_with_first;
	  }
	else
	  {
	    assert(!best_path_orbits.is_minimal_representative(search_stack[gca_level_with_best].split_element));
	    backjumping_level = gca_level_with_best;
	  }
	/* Backtrack */
	search_stack.resize(backjumping_level + 1);
	continue;
      }


      _INTERNAL_ERROR();


    handle_first_path_automorphism:
      /*
       *
       * A first-path automorphism: aut[i] = elements[first_path_labeling[i]]
       *
       */


      if(p.is_discrete())
	{
#if defined(BLISS_CONSISTENCY_CHECKS)
	  /* Verify that the complete automorphism is correctly built */
	  for(unsigned int i = 0; i < N; i++)
	    assert(first_path_automorphism[i] ==
		   p.elements[first_path_labeling[i]]);
#endif
	}
      else
	{
	  /* An automorphism that was found before the partition was discrete.
	   * Set the image of all elements in non-disrete cells accordingly */
	  for(Partition::Cell* c = p.first_nonsingleton_cell; c;
	      c = c->next_nonsingleton) {
	    for(unsigned int i = c->first; i < c->first+c->length; i++)
	      if(p.get_cell(p.elements[first_path_labeling[p.elements[i]]])->is_unit())
		first_path_automorphism[p.elements[first_path_labeling[p.elements[i]]]] = p.elements[i];
	      else
		first_path_automorphism[p.elements[i]] = p.elements[i];
	  }
	}

#if defined(BLISS_VERIFY_AUTOMORPHISMS)
      /* Verify that it really is an automorphism */
      if(!is_automorphism(first_path_automorphism))
	fatal_error("First path automorphism validation check failed");
#endif

      if(opt_use_long_prune)
	{
	  long_prune_add_automorphism(first_path_automorphism);
	}

      /*
       * Update orbit information
       */
      update_orbit_information(first_path_orbits, first_path_automorphism);

      /*
       * Compute backjumping level
       */
      for(unsigned int i = 0; i < search_stack.size(); i++) {
	TreeNode& n = search_stack[i];
	if(n.fp_on) {
	  ;
	} else {
	  n.fp_extendable = TreeNode::YES;
	}
      }

      /* Report automorphism by calling the user defined hook function */
      if(report_hook)
	(*report_hook)(report_user_param,
		       get_nof_vertices(),
		       first_path_automorphism);

      /* Update statistics */
      stats.nof_generators++;
      continue;

    } /* while(!search_stack.empty()) */


  /* Free "long prune" technique memory */
  if(opt_use_long_prune)
    long_prune_deallocate();

  /* Release component recursion data in partition */
  if(opt_use_comprec)
    p.cr_free();
}


void
AbstractGraph::find_automorphisms(Stats& stats,
				  void (*hook)(void *user_param,
					       unsigned int n,
					       const unsigned int *aut),
				  void *user_param)
{
  report_hook = hook;
  report_user_param = user_param;

  search(false, stats);

  if(first_path_labeling)
    {
      free(first_path_labeling);
      first_path_labeling = 0;
    }
  if(best_path_labeling)
    {
      free(best_path_labeling);
      best_path_labeling = 0;
    }
}


const unsigned int *
AbstractGraph::canonical_form(Stats& stats,
			      void (*hook)(void *user_param,
					   unsigned int n,
					   const unsigned int *aut),
			      void *user_param)
{

  report_hook = hook;
  report_user_param = user_param;

  search(true, stats);

  return best_path_labeling;
}


/*-------------------------------------------------------------------------
 *
 * Routines for directed graphs
 *
 *-------------------------------------------------------------------------*/

Digraph::Vertex::Vertex()
{
  color = 0;
}


Digraph::Vertex::~Vertex()
{
  ;
}


void
Digraph::Vertex::add_edge_to(const unsigned int other_vertex)
{
  edges_out.push_back(other_vertex);
}


void
Digraph::Vertex::add_edge_from(const unsigned int other_vertex)
{
  edges_in.push_back(other_vertex);
}


void
Digraph::Vertex::remove_duplicate_edges(std::vector<bool>& tmp)
{
#if defined(BLISS_CONSISTENCY_CHECKS)
  /* Pre-conditions  */
  for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
  for(std::vector<unsigned int>::iterator iter = edges_out.begin();
      iter != edges_out.end(); )
    {
      const unsigned int dest_vertex = *iter;
      if(tmp[dest_vertex] == true)
	{
	  /* A duplicate edge found! */
	  iter = edges_out.erase(iter);
	}
      else
	{
	  /* Not seen earlier, mark as seen */
	  tmp[dest_vertex] = true;
	  iter++;
	}
    }

  /* Clear tmp */
  for(std::vector<unsigned int>::iterator iter = edges_out.begin();
      iter != edges_out.end();
      iter++)
    {
      tmp[*iter] = false;
    }

  for(std::vector<unsigned int>::iterator iter = edges_in.begin();
      iter != edges_in.end(); )
    {
      const unsigned int dest_vertex = *iter;
      if(tmp[dest_vertex] == true)
	{
	  /* A duplicate edge found! */
	  iter = edges_in.erase(iter);
	}
      else
	{
	  /* Not seen earlier, mark as seen */
	  tmp[dest_vertex] = true;
	  iter++;
	}
    }

  /* Clear tmp */
  for(std::vector<unsigned int>::iterator iter = edges_in.begin();
      iter != edges_in.end();
      iter++)
    {
      tmp[*iter] = false;
    }
#if defined(BLISS_CONSISTENCY_CHECKS)
  /* Post-conditions  */
  for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
}


/**
 * Sort the edges entering and leaving the vertex according to
 * the vertex number of the other edge end.
 * Time complexity: O(e log(e)), where e is the number of edges
 * entering/leaving the vertex.
 */
void
Digraph::Vertex::sort_edges()
{
  std::sort(edges_in.begin(), edges_in.end());
  std::sort(edges_out.begin(), edges_out.end());
}


/*-------------------------------------------------------------------------
 *
 * Constructor and destructor for directed graphs
 *
 *-------------------------------------------------------------------------*/


Digraph::Digraph(const unsigned int nof_vertices)
{
  vertices.resize(nof_vertices);
  sh = shs_flm;
}


Digraph::~Digraph()
{
  ;
}


unsigned int
Digraph::add_vertex(const unsigned int color)
{
  const unsigned int new_vertex_num = vertices.size();
  vertices.resize(new_vertex_num + 1);
  vertices.back().color = color;
  return new_vertex_num;
}


void
Digraph::add_edge(const unsigned int vertex1, const unsigned int vertex2)
{
  assert(vertex1 < get_nof_vertices());
  assert(vertex2 < get_nof_vertices());
  vertices[vertex1].add_edge_to(vertex2);
  vertices[vertex2].add_edge_from(vertex1);
}


void
Digraph::change_color(const unsigned int vertex, const unsigned int new_color)
{
  assert(vertex < get_nof_vertices());
  vertices[vertex].color = new_color;
}


void
Digraph::sort_edges()
{
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    vertices[i].sort_edges();
}


int
Digraph::cmp(Digraph& other)
{
  /* Compare the numbers of vertices */
  if(get_nof_vertices() < other.get_nof_vertices())
    return -1;
  if(get_nof_vertices() > other.get_nof_vertices())
    return 1;
  /* Compare vertex colors */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      if(vertices[i].color < other.vertices[i].color)
	return -1;
      if(vertices[i].color > other.vertices[i].color)
	return 1;
    }
  /* Compare vertex degrees */
  remove_duplicate_edges();
  other.remove_duplicate_edges();
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      if(vertices[i].nof_edges_in() < other.vertices[i].nof_edges_in())
	return -1;
      if(vertices[i].nof_edges_in() > other.vertices[i].nof_edges_in())
	return 1;
      if(vertices[i].nof_edges_out() < other.vertices[i].nof_edges_out())
	return -1;
      if(vertices[i].nof_edges_out() > other.vertices[i].nof_edges_out())
	return 1;
    }
  /* Compare edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex& v1 = vertices[i];
      Vertex& v2 = other.vertices[i];
      v1.sort_edges();
      v2.sort_edges();
      std::vector<unsigned int>::const_iterator ei1 = v1.edges_in.begin();
      std::vector<unsigned int>::const_iterator ei2 = v2.edges_in.begin();
      while(ei1 != v1.edges_in.end())
	{
	  if(*ei1 < *ei2)
	    return -1;
	  if(*ei1 > *ei2)
	    return 1;
	  ei1++;
	  ei2++;
	}
      ei1 = v1.edges_out.begin();
      ei2 = v2.edges_out.begin();
      while(ei1 != v1.edges_out.end())
	{
	  if(*ei1 < *ei2)
	    return -1;
	  if(*ei1 > *ei2)
	    return 1;
	  ei1++;
	  ei2++;
	}
    }
  return 0;
}


Digraph*
Digraph::permute(const std::vector<unsigned int>& perm) const
{
  Digraph* const g = new Digraph(get_nof_vertices());
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex& v = vertices[i];
      g->change_color(perm[i], v.color);
      for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
	  ei != v.edges_out.end();
	  ei++)
	{
	  g->add_edge(perm[i], perm[*ei]);
	}
    }
  g->sort_edges();
  return g;
}


Digraph*
Digraph::permute(const unsigned int* const perm) const
{
  Digraph* const g = new Digraph(get_nof_vertices());
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex &v = vertices[i];
      g->change_color(perm[i], v.color);
      for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
	  ei != v.edges_out.end();
	  ei++)
	{
	  g->add_edge(perm[i], perm[*ei]);
	}
    }
  g->sort_edges();
  return g;
}


/*-------------------------------------------------------------------------
 *
 * Print graph in graphviz format
 *
 *-------------------------------------------------------------------------*/


#if 0
void
Digraph::write_dot(const char* const filename)
{
  FILE* const fp = fopen(filename, "w");
  if(fp)
    {
      write_dot(fp);
      fclose(fp);
    }
}


void
Digraph::write_dot(FILE* const fp)
{
  remove_duplicate_edges();

  fprintf(fp, "digraph g {\n");

  unsigned int vnum = 0;
  for(std::vector<Vertex>::const_iterator vi = vertices.begin();
      vi != vertices.end();
      vi++, vnum++)
    {
      const Vertex& v = *vi;
      fprintf(fp, "v%u [label=\"%u:%u\"];\n", vnum, vnum, v.color);
      for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
	  ei != v.edges_out.end();
	  ei++)
	{
	  fprintf(fp, "v%u -> v%u\n", vnum, *ei);
	}
    }

  fprintf(fp, "}\n");
}
#endif


void
Digraph::remove_duplicate_edges()
{
  std::vector<bool> tmp(get_nof_vertices(), false);

  for(std::vector<Vertex>::iterator vi = vertices.begin();
      vi != vertices.end();
      vi++)
    {
#if defined(BLISS_EXPENSIVE_CONSISTENCY_CHECKS)
      for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
      (*vi).remove_duplicate_edges(tmp);
    }
}


/*-------------------------------------------------------------------------
 *
 * Get a hash value for the graph.
 *
 *-------------------------------------------------------------------------*/

unsigned int
Digraph::get_hash()
{
  remove_duplicate_edges();
  sort_edges();

  UintSeqHash h;

  h.update(get_nof_vertices());

  /* Hash the color of each vertex */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      h.update(vertices[i].color);
    }

  /* Hash the edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v = vertices[i];
      for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
	  ei != v.edges_out.end();
	  ei++)
	{
	  h.update(i);
	  h.update(*ei);
	}
    }

  return h.get_value();
}


/*-------------------------------------------------------------------------
 *
 * Read directed graph in the DIMACS format.
 * Returns 0 if an error occurred.
 *
 *-------------------------------------------------------------------------*/

#if 0
Digraph*
Digraph::read_dimacs(FILE* const fp, FILE* const errstr)
{
  Digraph* g = 0;
  unsigned int nof_vertices;
  unsigned int nof_edges;
  unsigned int line_num = 1;

  const bool verbose = false;
  FILE* const verbstr = stdout;

  /* Read comments and the problem definition line */
  while(1)
    {
      int c = getc(fp);
      if(c == 'c')
	{
	  /* A comment, ignore the rest of the line */
	  while((c = getc(fp)) != '\n')
	    {
	      if(c == EOF) {
		if(errstr)
		  fprintf(errstr, "error in line %u: not in DIMACS format\n",
			  line_num);
		goto error_exit;
	      }
	    }
	  line_num++;
	  continue;
	}
      if(c == 'p')
	{
	  /* The problem definition line */
	  if(fscanf(fp, " edge %u %u\n", &nof_vertices, &nof_edges) != 2)
	    {
	      if(errstr)
		fprintf(errstr, "error in line %u: not in DIMACS format\n",
			line_num);
	      goto error_exit;
	    }
	  line_num++;
	  break;
	}
      if(errstr)
	fprintf(errstr, "error in line %u: not in DIMACS format\n", line_num);
      goto error_exit;
    }

  if(nof_vertices <= 0)
    {
      if(errstr)
	fprintf(errstr, "error: no vertices\n");
      goto error_exit;
    }
  if(verbose)
    {
      fprintf(verbstr, "Instance has %d vertices and %d edges\n",
	      nof_vertices, nof_edges);
      fflush(verbstr);
    }

  g = new Digraph(nof_vertices);

  //
  // Read vertex colors
  //
  if(verbose)
    {
      fprintf(verbstr, "Reading vertex colors...\n");
      fflush(verbstr);
    }
  while(1)
    {
      int c = getc(fp);
      if(c != 'n')
	{
	  ungetc(c, fp);
	  break;
	}
      ungetc(c, fp);
      unsigned int vertex;
      unsigned int color;
      if(fscanf(fp, "n %u %u\n", &vertex, &color) != 2)
	{
	  if(errstr)
	    fprintf(errstr, "error in line %u: not in DIMACS format\n",
		    line_num);
	  goto error_exit;
	}
      if(!((vertex >= 1) && (vertex <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...%u]\n",
		    line_num, vertex, nof_vertices);
	  goto error_exit;
	}
      line_num++;
      g->change_color(vertex - 1, color);
    }
  if(verbose)
    {
      fprintf(verbstr, "Done\n");
      fflush(verbstr);
    }

  //
  // Read edges
  //
  if(verbose)
    {
      fprintf(verbstr, "Reading edges...\n");
      fflush(verbstr);
    }
  for(unsigned i = 0; i < nof_edges; i++)
    {
      unsigned int from, to;
      if(fscanf(fp, "e %u %u\n", &from, &to) != 2)
	{
	  if(errstr)
	    fprintf(errstr, "error in line %u: not in DIMACS format\n",
		    line_num);
	  goto error_exit;
	}
      if(not((1 <= from) and (from <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...%u]\n",
		    line_num, from, nof_vertices);
	  goto error_exit;
	}
      if(not((1 <= to) and (to <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...%u]\n",
		    line_num, to, nof_vertices);
	  goto error_exit;
	}
      line_num++;
      g->add_edge(from-1, to-1);
    }
  if(verbose)
    {
      fprintf(verbstr, "Done\n");
      fflush(verbstr);
    }

  return g;

 error_exit:
  if(g)
    delete g;
  return 0;
}
#endif


#if 0
void
Digraph::write_dimacs(FILE* const fp)
{
  remove_duplicate_edges();
  sort_edges();

  /* First count the total number of edges */
  unsigned int nof_edges = 0;
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      nof_edges += vertices[i].edges_out.size();
    }

  /* Output the "header" line */
  fprintf(fp, "p edge %u %u\n", get_nof_vertices(), nof_edges);

  /* Print the color of each vertex */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex& v = vertices[i];
      fprintf(fp, "n %u %u\n", i+1, v.color);
      /*
      if(v.color != 0)
	{
	  fprintf(fp, "n %u %u\n", i+1, v.color);
	}
      */
    }

  /* Print the edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex& v = vertices[i];
      for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
	  ei != v.edges_out.end();
	  ei++)
	{
	  fprintf(fp, "e %u %u\n", i+1, (*ei)+1);
	}
    }
}
#endif


/*-------------------------------------------------------------------------
 *
 * Partition independent invariants
 *
 *-------------------------------------------------------------------------*/

unsigned int
Digraph::vertex_color_invariant(const Digraph* const g, const unsigned int vnum)
{
  return g->vertices[vnum].color;
}

unsigned int
Digraph::indegree_invariant(const Digraph* const g, const unsigned int vnum)
{
  return g->vertices[vnum].nof_edges_in();
}

unsigned int
Digraph::outdegree_invariant(const Digraph* const g, const unsigned int vnum)
{
  return g->vertices[vnum].nof_edges_out();
}

unsigned int
Digraph::selfloop_invariant(const Digraph* const g, const unsigned int vnum)
{
  /* Quite inefficient but luckily not in the critical path */
  const Vertex& v = g->vertices[vnum];
  for(std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
      ei != v.edges_out.end();
      ei++)
    {
      if(*ei == vnum)
	return 1;
    }
  return 0;
}


/*-------------------------------------------------------------------------
 *
 * Refine the partition p according to a partition independent invariant
 *
 *-------------------------------------------------------------------------*/

bool
Digraph::refine_according_to_invariant(unsigned int (*inv)(const Digraph* const g,
							   const unsigned int v))
{
  bool refined = false;

  for(Partition::Cell* cell = p.first_nonsingleton_cell; cell; )
    {

      Partition::Cell* const next_cell = cell->next_nonsingleton;
      const unsigned int* ep = p.elements + cell->first;
      for(unsigned int i = cell->length; i > 0; i--, ep++)
	{
	  unsigned int ival = inv(this, *ep);
	  p.invariant_values[*ep] = ival;
	  if(ival > cell->max_ival) {
	    cell->max_ival = ival;
	    cell->max_ival_count = 1;
	  }
	  else if(ival == cell->max_ival) {
	    cell->max_ival_count++;
	  }
	}
      Partition::Cell* const last_new_cell = p.zplit_cell(cell, true);
      refined |= (last_new_cell != cell);
      cell = next_cell;
    }

  return refined;
}


/*-------------------------------------------------------------------------
 *
 * Split the neighbourhood of a cell according to the equitable invariant
 *
 *-------------------------------------------------------------------------*/

bool
Digraph::split_neighbourhood_of_cell(Partition::Cell* const cell)
{


  const bool was_equal_to_first = refine_equal_to_first;

  if(compute_eqref_hash)
    {
      eqref_hash.update(cell->first);
      eqref_hash.update(cell->length);
    }

  const unsigned int* ep = p.elements + cell->first;
  for(unsigned int i = cell->length; i > 0; i--)
    {
      const Vertex& v = vertices[*ep++];

      std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j != 0; j--)
	{
	  const unsigned int dest_vertex = *ei++;
	  Partition::Cell* const neighbour_cell = p.get_cell(dest_vertex);
	  if(neighbour_cell->is_unit())
	    continue;
	  const unsigned int ival = ++p.invariant_values[dest_vertex];
	  if(ival > neighbour_cell->max_ival) {
	    neighbour_cell->max_ival = ival;
	    neighbour_cell->max_ival_count = 1;
	    if(ival == 1)
	      neighbour_heap.insert(neighbour_cell->first);
	  }
	  else if(ival == neighbour_cell->max_ival) {
	    neighbour_cell->max_ival_count++;
	  }
	}
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* const neighbour_cell = p.get_cell(p.elements[start]);

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}


      Partition::Cell* const last_new_cell = p.zplit_cell(neighbour_cell, true);

      /* Update certificate and hash if needed */
      const Partition::Cell* c = neighbour_cell;
      while(1)
	{
	  if(in_search)
	    {
	      /* Build certificate */
	      cert_add_redundant(CERT_SPLIT, c->first, c->length);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	  if(compute_eqref_hash)
	    {
	      eqref_hash.update(c->first);
	      eqref_hash.update(c->length);
	    }
	  if(c == last_new_cell)
	    break;
	  c = c->next;
	}
    }

  if(cell->is_in_splitting_queue())
    {
      return false;
    }


  ep = p.elements + cell->first;
  for(unsigned int i = cell->length; i > 0; i--)
    {
      const Vertex& v = vertices[*ep++];

      std::vector<unsigned int>::const_iterator ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  const unsigned int dest_vertex = *ei++;
	  Partition::Cell* const neighbour_cell = p.get_cell(dest_vertex);
	  if(neighbour_cell->is_unit())
	    continue;
	  const unsigned int ival = ++p.invariant_values[dest_vertex];
	  if(ival > neighbour_cell->max_ival)
	    {
	      neighbour_cell->max_ival = ival;
	      neighbour_cell->max_ival_count = 1;
	      if(ival == 1)
		neighbour_heap.insert(neighbour_cell->first);
	    }
	  else if(ival == neighbour_cell->max_ival) {
	    neighbour_cell->max_ival_count++;
	  }
	}
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* const neighbour_cell = p.get_cell(p.elements[start]);

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}

      Partition::Cell* const last_new_cell = p.zplit_cell(neighbour_cell, true);

      /* Update certificate and hash if needed */
      const Partition::Cell* c = neighbour_cell;
      while(1)
	{
	  if(in_search)
	    {
	      /* Build certificate */
	      cert_add_redundant(CERT_SPLIT, c->first, c->length);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	  if(compute_eqref_hash)
	    {
	      eqref_hash.update(c->first);
	      eqref_hash.update(c->length);
	    }
	  if(c == last_new_cell)
	    break;
	  c = c->next;
	}
    }


  if(refine_compare_certificate and
     (refine_equal_to_first == false) and
     (refine_cmp_to_best < 0))
    return true;

  return false;

 worse_exit:
  /* Clear neighbour heap */
  UintSeqHash rest;
  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* const neighbour_cell = p.get_cell(p.elements[start]);
      if(opt_use_failure_recording and was_equal_to_first)
	{
	  rest.update(neighbour_cell->first);
	  rest.update(neighbour_cell->length);
	  rest.update(neighbour_cell->max_ival);
	  rest.update(neighbour_cell->max_ival_count);
	}
      neighbour_cell->max_ival = 0;
      neighbour_cell->max_ival_count = 0;
      p.clear_ivs(neighbour_cell);
    }
  if(opt_use_failure_recording and was_equal_to_first)
    {
      for(unsigned int i = p.splitting_queue.size(); i > 0; i--)
	{
	  Partition::Cell* const cell = p.splitting_queue.pop_front();
	  rest.update(cell->first);
	  rest.update(cell->length);
	  p.splitting_queue.push_back(cell);
	}
      rest.update(failure_recording_fp_deviation);
      failure_recording_fp_deviation = rest.get_value();
    }

   return true;
}


bool
Digraph::split_neighbourhood_of_unit_cell(Partition::Cell* const unit_cell)
{


  const bool was_equal_to_first = refine_equal_to_first;

  if(compute_eqref_hash)
    {
      eqref_hash.update(0x87654321);
      eqref_hash.update(unit_cell->first);
      eqref_hash.update(1);
    }

  const Vertex& v = vertices[p.elements[unit_cell->first]];

  /*
   * Phase 1
   * Refine neighbours according to the edges that leave the vertex v
   */
  std::vector<unsigned int>::const_iterator ei = v.edges_out.begin();
  for(unsigned int j = v.nof_edges_out(); j > 0; j--)
    {
      const unsigned int dest_vertex = *ei++;
      Partition::Cell* const neighbour_cell = p.get_cell(dest_vertex);

      if(neighbour_cell->is_unit()) {
	if(in_search) {
	  /* Remember neighbour in order to generate certificate */
	  neighbour_heap.insert(neighbour_cell->first);
	}
	continue;
      }
      if(neighbour_cell->max_ival_count == 0)
	{
	  neighbour_heap.insert(neighbour_cell->first);
	}
      neighbour_cell->max_ival_count++;

      unsigned int* const swap_position =
	p.elements + neighbour_cell->first + neighbour_cell->length -
	neighbour_cell->max_ival_count;
      *p.in_pos[dest_vertex] = *swap_position;
      p.in_pos[*swap_position] = p.in_pos[dest_vertex];
      *swap_position = dest_vertex;
      p.in_pos[dest_vertex] = swap_position;
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* neighbour_cell =	p.get_cell(p.elements[start]);

#if defined(BLISS_CONSISTENCY_CHECKS)
      assert(neighbour_cell->first == start);
      if(neighbour_cell->is_unit()) {
	assert(neighbour_cell->max_ival_count == 0);
      } else {
	assert(neighbour_cell->max_ival_count > 0);
	assert(neighbour_cell->max_ival_count <= neighbour_cell->length);
      }
#endif

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}

      if(neighbour_cell->length > 1 and
	 neighbour_cell->max_ival_count != neighbour_cell->length)
	{

	  Partition::Cell* const new_cell =
	    p.aux_split_in_two(neighbour_cell,
			       neighbour_cell->length -
			       neighbour_cell->max_ival_count);
	  unsigned int* ep = p.elements + new_cell->first;
	  unsigned int* const lp = p.elements+new_cell->first+new_cell->length;
	  while(ep < lp)
	    {
	      p.element_to_cell_map[*ep] = new_cell;
	      ep++;
	    }
	  neighbour_cell->max_ival_count = 0;


	  if(compute_eqref_hash)
	    {
	      /* Update hash */
	      eqref_hash.update(neighbour_cell->first);
	      eqref_hash.update(neighbour_cell->length);
	      eqref_hash.update(0);
	      eqref_hash.update(new_cell->first);
	      eqref_hash.update(new_cell->length);
	      eqref_hash.update(1);
	    }

	  /* Add cells in splitting_queue */
	  if(neighbour_cell->is_in_splitting_queue()) {
	    /* Both cells must be included in splitting_queue in order
	       to have refinement to equitable partition */
	    p.splitting_queue_add(new_cell);
	  } else {
	    Partition::Cell *min_cell, *max_cell;
	  if(neighbour_cell->length <= new_cell->length) {
	    min_cell = neighbour_cell;
	    max_cell = new_cell;
	  } else {
	    min_cell = new_cell;
	    max_cell = neighbour_cell;
	  }
	  /* Put the smaller cell in splitting_queue */
	   p.splitting_queue_add(min_cell);
	  if(max_cell->is_unit()) {
	    /* Put the "larger" cell also in splitting_queue */
	    p.splitting_queue_add(max_cell);
	  }
	}
	/* Update pointer for certificate generation */
	neighbour_cell = new_cell;
      }
      else
	{
	  neighbour_cell->max_ival_count = 0;
	}

      /*
       * Build certificate if required
       */
      if(in_search)
	{
	  for(unsigned int i = neighbour_cell->first,
		j = neighbour_cell->length;
	      j > 0;
	      j--, i++)
	    {
	      /* Build certificate */
	      cert_add(CERT_EDGE, unit_cell->first, i);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	} /* if(in_search) */
    } /* while(!neighbour_heap.is_empty()) */

  /*
   * Phase 2
   * Refine neighbours according to the edges that enter the vertex v
   */
  ei = v.edges_in.begin();
  for(unsigned int j = v.nof_edges_in(); j > 0; j--)
    {
      const unsigned int dest_vertex = *ei++;
      Partition::Cell* const neighbour_cell = p.get_cell(dest_vertex);

      if(neighbour_cell->is_unit()) {
	if(in_search) {
	  neighbour_heap.insert(neighbour_cell->first);
	}
	continue;
      }
      if(neighbour_cell->max_ival_count == 0)
	{
	  neighbour_heap.insert(neighbour_cell->first);
	}
      neighbour_cell->max_ival_count++;

      unsigned int* const swap_position =
	p.elements + neighbour_cell->first + neighbour_cell->length -
	neighbour_cell->max_ival_count;
      *p.in_pos[dest_vertex] = *swap_position;
      p.in_pos[*swap_position] = p.in_pos[dest_vertex];
      *swap_position = dest_vertex;
      p.in_pos[dest_vertex] = swap_position;
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* neighbour_cell =	p.get_cell(p.elements[start]);

#if defined(BLISS_CONSISTENCY_CHECKS)
      assert(neighbour_cell->first == start);
      if(neighbour_cell->is_unit()) {
	assert(neighbour_cell->max_ival_count == 0);
      } else {
	assert(neighbour_cell->max_ival_count > 0);
	assert(neighbour_cell->max_ival_count <= neighbour_cell->length);
      }
#endif

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}

      if(neighbour_cell->length > 1 and
	 neighbour_cell->max_ival_count != neighbour_cell->length)
	{
	  Partition::Cell* const new_cell =
	    p.aux_split_in_two(neighbour_cell,
			       neighbour_cell->length -
			       neighbour_cell->max_ival_count);
	  unsigned int* ep = p.elements + new_cell->first;
	  unsigned int* const lp = p.elements+new_cell->first+new_cell->length;
	  while(ep < lp) {
	    p.element_to_cell_map[*ep] = new_cell;
	    ep++;
	  }
	  neighbour_cell->max_ival_count = 0;


	  if(compute_eqref_hash)
	    {
	      eqref_hash.update(neighbour_cell->first);
	      eqref_hash.update(neighbour_cell->length);
	      eqref_hash.update(0);
	      eqref_hash.update(new_cell->first);
	      eqref_hash.update(new_cell->length);
	      eqref_hash.update(1);
	    }

	  /* Add cells in splitting_queue */
	  if(neighbour_cell->is_in_splitting_queue()) {
	    /* Both cells must be included in splitting_queue in order
	       to have refinement to equitable partition */
	    p.splitting_queue_add(new_cell);
	  } else {
	    Partition::Cell *min_cell, *max_cell;
	    if(neighbour_cell->length <= new_cell->length) {
	      min_cell = neighbour_cell;
	      max_cell = new_cell;
	    } else {
	      min_cell = new_cell;
	      max_cell = neighbour_cell;
	    }
	    /* Put the smaller cell in splitting_queue */
	    p.splitting_queue_add(min_cell);
	    if(max_cell->is_unit()) {
	      /* Put the "larger" cell also in splitting_queue */
	      p.splitting_queue_add(max_cell);
	    }
	  }
	  /* Update pointer for certificate generation */
	  neighbour_cell = new_cell;
	}
      else
	{
	  neighbour_cell->max_ival_count = 0;
	}

      /*
       * Build certificate if required
       */
      if(in_search)
	{
	  for(unsigned int i = neighbour_cell->first,
		j = neighbour_cell->length;
	      j > 0;
	      j--, i++)
	    {
	      /* Build certificate */
	      cert_add(CERT_EDGE, i, unit_cell->first);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	} /* if(in_search) */
    } /* while(!neighbour_heap.is_empty()) */

  if(refine_compare_certificate and
     (refine_equal_to_first == false) and
     (refine_cmp_to_best < 0))
    return true;

  return false;

 worse_exit:
  /* Clear neighbour heap */
  UintSeqHash rest;
  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* const neighbour_cell = p.get_cell(p.elements[start]);
      if(opt_use_failure_recording and was_equal_to_first)
	{
	  rest.update(neighbour_cell->first);
	  rest.update(neighbour_cell->length);
	  rest.update(neighbour_cell->max_ival_count);
	}
      neighbour_cell->max_ival_count = 0;
    }
  if(opt_use_failure_recording and was_equal_to_first)
    {
      rest.update(failure_recording_fp_deviation);
      failure_recording_fp_deviation = rest.get_value();
    }
  return true;
}


/*-------------------------------------------------------------------------
 *
 * Check whether the current partition p is equitable.
 * Performance: very slow, use only for debugging purposes.
 *
 *-------------------------------------------------------------------------*/

bool
Digraph::is_equitable() const
{
  const unsigned int N = get_nof_vertices();
  if(N == 0)
    return true;

  std::vector<unsigned int> first_count = std::vector<unsigned int>(N, 0);
  std::vector<unsigned int> other_count = std::vector<unsigned int>(N, 0);

  /*
   * Check equitabledness w.r.t. outgoing edges
   */
  for(Partition::Cell* cell = p.first_cell; cell; cell = cell->next)
    {
      if(cell->is_unit())
	continue;

      unsigned int* ep = p.elements + cell->first;
      const Vertex& first_vertex = vertices[*ep++];

      /* Count outgoing edges of the first vertex for cells */
      for(std::vector<unsigned int>::const_iterator ei =
	    first_vertex.edges_out.begin();
	  ei != first_vertex.edges_out.end();
	  ei++)
	{
	  first_count[p.get_cell(*ei)->first]++;
	}

      /* Count and compare outgoing edges of the other vertices */
      for(unsigned int i = cell->length; i > 1; i--)
	{
	  const Vertex &vertex = vertices[*ep++];
	  for(std::vector<unsigned int>::const_iterator ei =
		vertex.edges_out.begin();
	      ei != vertex.edges_out.end();
	      ei++)
	    {
	      other_count[p.get_cell(*ei)->first]++;
	    }
	  for(Partition::Cell *cell2 = p.first_cell;
	      cell2;
	      cell2 = cell2->next)
	    {
	      if(first_count[cell2->first] != other_count[cell2->first])
		{
		  /* Not equitable */
		  return false;
		}
	      other_count[cell2->first] = 0;
	    }
	}
      /* Reset first_count */
      for(unsigned int i = 0; i < N; i++)
	first_count[i] = 0;
    }


  /*
   * Check equitabledness w.r.t. incoming edges
   */
  for(Partition::Cell* cell = p.first_cell; cell; cell = cell->next)
    {
      if(cell->is_unit())
	continue;

      unsigned int* ep = p.elements + cell->first;
      const Vertex& first_vertex = vertices[*ep++];

      /* Count incoming edges of the first vertex for cells */
      for(std::vector<unsigned int>::const_iterator ei =
	    first_vertex.edges_in.begin();
	  ei != first_vertex.edges_in.end();
	  ei++)
	{
	  first_count[p.get_cell(*ei)->first]++;
	}

      /* Count and compare incoming edges of the other vertices */
      for(unsigned int i = cell->length; i > 1; i--)
	{
	  const Vertex &vertex = vertices[*ep++];
	  for(std::vector<unsigned int>::const_iterator ei =
		vertex.edges_in.begin();
	      ei != vertex.edges_in.end();
	      ei++)
	    {
	      other_count[p.get_cell(*ei)->first]++;
	    }
	  for(Partition::Cell *cell2 = p.first_cell;
	      cell2;
	      cell2 = cell2->next)
	    {
	      if(first_count[cell2->first] != other_count[cell2->first])
		{
		  /* Not equitable */
		  return false;
		}
	      other_count[cell2->first] = 0;
	    }
	}
      /* Reset first_count */
      for(unsigned int i = 0; i < N; i++)
	first_count[i] = 0;
    }
  return true;
}


/*-------------------------------------------------------------------------
 *
 * Build the initial equitable partition
 *
 *-------------------------------------------------------------------------*/

void
Digraph::make_initial_equitable_partition()
{
  refine_according_to_invariant(&vertex_color_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_according_to_invariant(&selfloop_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_according_to_invariant(&outdegree_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_according_to_invariant(&indegree_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_to_equitable();
  //p.print_signature(stderr); fprintf(stderr, "\n");
}


/*-------------------------------------------------------------------------
 *
 * Find the next cell to be splitted
 *
 *-------------------------------------------------------------------------*/

Partition::Cell*
Digraph::find_next_cell_to_be_splitted(Partition::Cell* cell)
{
  switch(sh) {
  case shs_f:   return sh_first();
  case shs_fs:  return sh_first_smallest();
  case shs_fl:  return sh_first_largest();
  case shs_fm:  return sh_first_max_neighbours();
  case shs_fsm: return sh_first_smallest_max_neighbours();
  case shs_flm: return sh_first_largest_max_neighbours();
  default:
    fatal_error("Internal error - unknown splitting heuristics");
    return 0;
  }
}

/** \internal
 * A splitting heuristic.
 * Returns the first nonsingleton cell in the current partition.
 * The argument \a cell is ignored.
 */
Partition::Cell*
Digraph::sh_first()
{
  Partition::Cell* best_cell = 0;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      best_cell = cell;
      break;
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first smallest nonsingleton cell in the current partition.
 * The argument \a cell is ignored.
 */
Partition::Cell*
Digraph::sh_first_smallest()
{
  Partition::Cell* best_cell = 0;
  unsigned int best_size = UINT_MAX;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      if(cell->length < best_size)
	{
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first largest nonsingleton cell in the current partition.
 * The argument \a cell is ignored.
 */
Partition::Cell*
Digraph::sh_first_largest()
{
  Partition::Cell* best_cell = 0;
  unsigned int best_size = 0;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      if(cell->length > best_size)
	{
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first nonsingleton cell with max number of neighbouring
 * nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Digraph::sh_first_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      int value = 0;
      const Vertex &v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei;
      ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  Partition::Cell * const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j > 0; j--)
	{
	  Partition::Cell * const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      if(value > best_value)
	{
	  best_value = value;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first smallest nonsingleton cell with max number of neighbouring
 * nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Digraph::sh_first_smallest_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  unsigned int best_size = UINT_MAX;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {

      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;

      int value = 0;
      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei;

      ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  Partition::Cell * const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell * const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j > 0; j--)
	{
	  Partition::Cell * const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell * const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      if((value > best_value) or
	 (value == best_value and cell->length < best_size))
	{
	  best_value = value;
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first largest nonsingleton cell with max number of neighbouring
 * nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Digraph::sh_first_largest_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  unsigned int best_size = 0;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {

      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;

      int value = 0;
      const Vertex &v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei;

      ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  Partition::Cell* const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j > 0; j--)
	{
	  Partition::Cell* const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}

      if((value > best_value) ||
	 (value == best_value && cell->length > best_size))
	{
	  best_value = value;
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}


/*------------------------------------------------------------------------
 *
 * Initialize the certificate size and memory
 *
 *-------------------------------------------------------------------------*/

void
Digraph::initialize_certificate()
{
  certificate_index = 0;
  certificate_current_path.clear();
  certificate_first_path.clear();
  certificate_best_path.clear();
}


/*
 * Check whether perm is an automorphism.
 * Slow, mainly for debugging and validation purposes.
 */
bool
Digraph::is_automorphism(unsigned int* const perm)
{
  std::set<unsigned int, std::less<unsigned int> > edges1;
  std::set<unsigned int, std::less<unsigned int> > edges2;

#if defined(BLISS_CONSISTENCY_CHECKS)
  if(!is_permutation(get_nof_vertices(), perm))
    _INTERNAL_ERROR();
#endif

  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex& v1 = vertices[i];
      Vertex& v2 = vertices[perm[i]];

      edges1.clear();
      for(std::vector<unsigned int>::iterator ei = v1.edges_in.begin();
	  ei != v1.edges_in.end();
	  ei++)
	edges1.insert(perm[*ei]);
      edges2.clear();
      for(std::vector<unsigned int>::iterator ei = v2.edges_in.begin();
	  ei != v2.edges_in.end();
	  ei++)
	edges2.insert(*ei);
      if(!(edges1 == edges2))
	return false;

      edges1.clear();
      for(std::vector<unsigned int>::iterator ei = v1.edges_out.begin();
	  ei != v1.edges_out.end();
	  ei++)
	edges1.insert(perm[*ei]);
      edges2.clear();
      for(std::vector<unsigned int>::iterator ei = v2.edges_out.begin();
	  ei != v2.edges_out.end();
	  ei++)
	edges2.insert(*ei);
      if(!(edges1 == edges2))
	return false;
    }

  return true;
}

bool
Digraph::is_automorphism(const std::vector<unsigned int>& perm) const
{

  if(!(perm.size() == get_nof_vertices() and is_permutation(perm)))
    return false;

  std::set<unsigned int, std::less<unsigned int> > edges1;
  std::set<unsigned int, std::less<unsigned int> > edges2;

  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex& v1 = vertices[i];
      const Vertex& v2 = vertices[perm[i]];

      edges1.clear();
      for(std::vector<unsigned int>::const_iterator ei = v1.edges_in.begin();
	  ei != v1.edges_in.end();
	  ei++)
	edges1.insert(perm[*ei]);
      edges2.clear();
      for(std::vector<unsigned int>::const_iterator ei = v2.edges_in.begin();
	  ei != v2.edges_in.end();
	  ei++)
	edges2.insert(*ei);
      if(!(edges1 == edges2))
	return false;

      edges1.clear();
      for(std::vector<unsigned int>::const_iterator ei = v1.edges_out.begin();
	  ei != v1.edges_out.end();
	  ei++)
	edges1.insert(perm[*ei]);
      edges2.clear();
      for(std::vector<unsigned int>::const_iterator ei = v2.edges_out.begin();
	  ei != v2.edges_out.end();
	  ei++)
	edges2.insert(*ei);
      if(!(edges1 == edges2))
	return false;
    }

  return true;
}


bool
Digraph::nucr_find_first_component(const unsigned int level)
{

  cr_component.clear();
  cr_component_elements = 0;

  /* Find first non-discrete cell in the component level */
  Partition::Cell* first_cell = p.first_nonsingleton_cell;
  while(first_cell)
    {
      if(p.cr_get_level(first_cell->first) == level)
	break;
      first_cell = first_cell->next_nonsingleton;
    }

  /* The component is discrete, return false */
  if(!first_cell)
    return false;

  std::vector<Partition::Cell*> component;
  first_cell->max_ival = 1;
  component.push_back(first_cell);

  for(unsigned int i = 0; i < component.size(); i++)
    {
      Partition::Cell* const cell = component[i];

      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei;

      ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;
	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);

	  /* Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Already marked to be in the same component? */
	  if(neighbour_cell->max_ival == 1)
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  if(p.cr_get_level(neighbour_cell->first) != level)
	    continue;

	  if(neighbour_cell->max_ival_count == 0)
	    neighbour_heap.insert(neighbour_cell->first);
	  neighbour_cell->max_ival_count++;
	}
      while(!neighbour_heap.is_empty())
	{
	  const unsigned int start = neighbour_heap.remove();
	  Partition::Cell* const neighbour_cell =
	    p.get_cell(p.elements[start]);

	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  neighbour_cell->max_ival_count = 0;
	  neighbour_cell->max_ival = 1;
	  component.push_back(neighbour_cell);
	}

      ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;

	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);

	  /* Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Already marked to be in the same component? */
	  if(neighbour_cell->max_ival == 1)
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  if(p.cr_get_level(neighbour_cell->first) != level)
	    continue;

	  if(neighbour_cell->max_ival_count == 0)
	    neighbour_heap.insert(neighbour_cell->first);
	  neighbour_cell->max_ival_count++;
	}
      while(!neighbour_heap.is_empty())
	{
	  const unsigned int start = neighbour_heap.remove();
	  Partition::Cell* const neighbour_cell =
	    p.get_cell(p.elements[start]);

	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  neighbour_cell->max_ival_count = 0;
	  neighbour_cell->max_ival = 1;
	  component.push_back(neighbour_cell);
	}
    }

  for(unsigned int i = 0; i < component.size(); i++)
    {
      Partition::Cell* const cell = component[i];
      cell->max_ival = 0;
      cr_component.push_back(cell->first);
      cr_component_elements += cell->length;
    }

  return true;
}


bool
Digraph::nucr_find_first_component(const unsigned int level,
				 std::vector<unsigned int>& component,
				 unsigned int& component_elements,
				 Partition::Cell*& sh_return)
{

  component.clear();
  component_elements = 0;
  sh_return = 0;
  unsigned int sh_first  = 0;
  unsigned int sh_size   = 0;
  unsigned int sh_nuconn = 0;

  /* Find first non-discrete cell in the component level */
  Partition::Cell* first_cell = p.first_nonsingleton_cell;
  while(first_cell)
    {
      if(p.cr_get_level(first_cell->first) == level)
	break;
      first_cell = first_cell->next_nonsingleton;
    }

  if(!first_cell)
    {
      /* The component is discrete, return false */
      return false;
    }

  std::vector<Partition::Cell*> comp;
  KStack<Partition::Cell*> neighbours;
  neighbours.init(get_nof_vertices());

  first_cell->max_ival = 1;
  comp.push_back(first_cell);

  for(unsigned int i = 0; i < comp.size(); i++)
    {
      Partition::Cell* const cell = comp[i];

      unsigned int nuconn = 1;

      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei;

      /*| Phase 1: outgoing edges */
      ei = v.edges_out.begin();
      for(unsigned int j = v.nof_edges_out(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;

	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);

	  /* Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  //if(p.cr_get_level(neighbour_cell->first) != level)
	  //  continue;
	  if(neighbour_cell->max_ival_count == 0)
	    neighbours.push(neighbour_cell);
	  neighbour_cell->max_ival_count++;
	}
      while(!neighbours.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbours.pop();
	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  nuconn++;
	  neighbour_cell->max_ival_count = 0;
	  if(neighbour_cell->max_ival == 0) {
	    comp.push_back(neighbour_cell);
	    neighbour_cell->max_ival = 1;
	  }
	}

      /*| Phase 2: incoming edges */
      ei = v.edges_in.begin();
      for(unsigned int j = v.nof_edges_in(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;
	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);
	  /*| Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  //if(p.cr_get_level(neighbour_cell->first) != level)
	  //  continue;
	  if(neighbour_cell->max_ival_count == 0)
	    neighbours.push(neighbour_cell);
	  neighbour_cell->max_ival_count++;
	}
      while(!neighbours.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbours.pop();
	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  nuconn++;
	  neighbour_cell->max_ival_count = 0;
	  if(neighbour_cell->max_ival == 0) {
	    comp.push_back(neighbour_cell);
	    neighbour_cell->max_ival = 1;
	  }
	}

      /*| Phase 3: splitting heuristics */
      switch(sh) {
      case shs_f:
	if(sh_return == 0 or
	   cell->first <= sh_first) {
	  sh_return = cell;
	  sh_first = cell->first;
	}
	break;
      case shs_fs:
	if(sh_return == 0 or
	   cell->length < sh_size or
	   (cell->length == sh_size and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	}
	break;
      case shs_fl:
	if(sh_return == 0 or
	   cell->length > sh_size or
	   (cell->length == sh_size and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	}
	break;
      case shs_fm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_nuconn = nuconn;
	}
	break;
      case shs_fsm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and
	    (cell->length < sh_size or
	     (cell->length == sh_size and cell->first <= sh_first)))) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	  sh_nuconn = nuconn;
	}
	break;
      case shs_flm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and
	    (cell->length > sh_size or
	     (cell->length == sh_size and cell->first <= sh_first)))) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	  sh_nuconn = nuconn;
	}
	break;
      default:
	fatal_error("Internal error - unknown splitting heuristics");
	return 0;
      }
    }
  assert(sh_return);

  for(unsigned int i = 0; i < comp.size(); i++)
    {
      Partition::Cell* const cell = comp[i];
      cell->max_ival = 0;
      component.push_back(cell->first);
      component_elements += cell->length;
    }

  return true;
}


/*-------------------------------------------------------------------------
 *
 * Routines for undirected graphs
 *
 *-------------------------------------------------------------------------*/

Graph::Vertex::Vertex()
{
  color = 0;
}


Graph::Vertex::~Vertex()
{
  ;
}


void
Graph::Vertex::add_edge(const unsigned int other_vertex)
{
  edges.push_back(other_vertex);
}


void
Graph::Vertex::remove_duplicate_edges(std::vector<bool>& tmp)
{
#if defined(BLISS_CONSISTENCY_CHECKS)
  /* Pre-conditions  */
  for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
  for(std::vector<unsigned int>::iterator iter = edges.begin();
      iter != edges.end(); )
    {
      const unsigned int dest_vertex = *iter;
      if(tmp[dest_vertex] == true)
	{
	  /* A duplicate edge found! */
	  iter = edges.erase(iter);
	}
      else
	{
	  /* Not seen earlier, mark as seen */
	  tmp[dest_vertex] = true;
	  iter++;
	}
    }

  /* Clear tmp */
  for(std::vector<unsigned int>::iterator iter = edges.begin();
      iter != edges.end();
      iter++)
    {
      tmp[*iter] = false;
    }
#if defined(BLISS_CONSISTENCY_CHECKS)
  /* Post-conditions  */
  for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
}


/**
 * Sort the edges leaving the vertex according to
 * the vertex number of the other edge end.
 * Time complexity: O(e log(e)), where e is the number of edges
 * leaving the vertex.
 */
void
Graph::Vertex::sort_edges()
{
  std::sort(edges.begin(), edges.end());
}


/*-------------------------------------------------------------------------
 *
 * Constructor and destructor for undirected graphs
 *
 *-------------------------------------------------------------------------*/


Graph::Graph(const unsigned int nof_vertices)
{
  vertices.resize(nof_vertices);
  sh = shs_flm;
}


Graph::~Graph()
{
  ;
}


unsigned int
Graph::add_vertex(const unsigned int color)
{
  const unsigned int vertex_num = vertices.size();
  vertices.resize(vertex_num + 1);
  vertices.back().color = color;
  return vertex_num;
}


void
Graph::add_edge(const unsigned int vertex1, const unsigned int vertex2)
{
  //fprintf(stderr, "(%u,%u) ", vertex1, vertex2);
  vertices[vertex1].add_edge(vertex2);
  vertices[vertex2].add_edge(vertex1);
}


void
Graph::change_color(const unsigned int vertex, const unsigned int color)
{
  vertices[vertex].color = color;
}


/*-------------------------------------------------------------------------
 *
 * Read graph in the DIMACS format.
 * Returns 0 if an error occurred.
 *
 *-------------------------------------------------------------------------*/

#if 0
Graph*
Graph::read_dimacs(FILE* const fp, FILE* const errstr)
{
  Graph *g = 0;
  unsigned int nof_vertices;
  unsigned int nof_edges;
  unsigned int line_num = 1;
  int c;

  const bool verbose = false;
  FILE* const verbstr = stdout;

  /* Read comments and the problem definition line */
  while(1)
    {
      c = getc(fp);
      if(c == 'c')
	{
	  /* A comment, ignore the rest of the line */
	  while((c = getc(fp)) != '\n')
	    {
	      if(c == EOF)
		{
		  if(errstr)
		    fprintf(errstr,
			    "error in line %u: not in DIMACS format\n",
			    line_num);
		  goto error_exit;
		}
	    }
	  line_num++;
	  continue;
	}
      if(c == 'p')
	{
	  /* The problem definition line */
	  if(fscanf(fp, " edge %u %u\n", &nof_vertices, &nof_edges) != 2)
	    {
	      if(errstr)
		fprintf(errstr, "error in line %u: not in DIMACS format\n",
			line_num);
	      goto error_exit;
	    }
	  line_num++;
	  break;
	}
      if(errstr)
	fprintf(errstr, "error in line %u: not in DIMACS format\n", line_num);
      goto error_exit;
    }

  if(nof_vertices <= 0)
    {
      if(errstr)
	fprintf(errstr, "error: no vertices\n");
      goto error_exit;
    }
  if(verbose)
    {
      fprintf(verbstr, "Instance has %d vertices and %d edges\n",
	      nof_vertices, nof_edges);
      fflush(verbstr);
    }

  g = new Graph(nof_vertices);

  //
  // Read vertex colors
  //
  if(verbose)
    {
      fprintf(verbstr, "Reading vertex colors...\n");
      fflush(verbstr);
    }
  while(1)
    {
      c = getc(fp);
      if(c != 'n')
	{
	  ungetc(c, fp);
	  break;
	}
      ungetc(c, fp);
      unsigned int vertex;
      unsigned int color;
      if(fscanf(fp, "n %u %u\n", &vertex, &color) != 2)
	{
	  if(errstr)
	    fprintf(errstr, "error in line %u: not in DIMACS format\n",
		    line_num);
	  goto error_exit;
	}
      if(!((vertex >= 1) && (vertex <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...,%u]\n",
		    line_num, vertex, nof_vertices);
	  goto error_exit;
	}
      line_num++;
      g->change_color(vertex - 1, color);
    }
  if(verbose)
    {
      fprintf(verbstr, "Done\n");
      fflush(verbstr);
    }

  //
  // Read edges
  //
  if(verbose)
    {
      fprintf(verbstr, "Reading edges...\n");
      fflush(verbstr);
    }
  for(unsigned i = 0; i < nof_edges; i++)
    {
      unsigned int from, to;
      if(fscanf(fp, "e %u %u\n", &from, &to) != 2)
	{
	  if(errstr)
	    fprintf(errstr, "error in line %u: not in DIMACS format\n",
		    line_num);
	  goto error_exit;
	}
      if(!((from >= 1) && (from <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...,%u]\n",
		    line_num, from, nof_vertices);
	  goto error_exit;
	}
      if(!((to >= 1) && (to <= nof_vertices)))
	{
	  if(errstr)
	    fprintf(errstr,
		    "error in line %u: vertex %u not in range [1,...,%u]\n",
		    line_num, to, nof_vertices);
	  goto error_exit;
	}
      line_num++;
      g->add_edge(from-1, to-1);
    }
  if(verbose)
    {
      fprintf(verbstr, "Done\n");
      fflush(verbstr);
    }

  return g;

 error_exit:
  if(g)
    delete g;
  return 0;

}


void
Graph::write_dimacs(FILE* const fp)
{
  remove_duplicate_edges();
  sort_edges();

  /* First count the total number of edges */
  unsigned int nof_edges = 0;
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v = vertices[i];
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int dest_i = *ei;
	  if(dest_i < i)
	    continue;
	  nof_edges++;
	}
    }

  /* Output the "header" line */
  fprintf(fp, "p edge %u %u\n", get_nof_vertices(), nof_edges);

  /* Print the color of each vertex */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v = vertices[i];
      fprintf(fp, "n %u %u\n", i+1, v.color);
      /*
      if(v.color != 0)
	{
	  fprintf(fp, "n %u %u\n", i+1, v.color);
	}
      */
    }

  /* Print the edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v = vertices[i];
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int dest_i = *ei;
	  if(dest_i < i)
	    continue;
	  fprintf(fp, "e %u %u\n", i+1, dest_i+1);
	}
    }
}
#endif


void
Graph::sort_edges()
{
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    vertices[i].sort_edges();
}


int
Graph::cmp(Graph& other)
{
  /* Compare the numbers of vertices */
  if(get_nof_vertices() < other.get_nof_vertices())
    return -1;
  if(get_nof_vertices() > other.get_nof_vertices())
    return 1;
  /* Compare vertex colors */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      if(vertices[i].color < other.vertices[i].color)
	return -1;
      if(vertices[i].color > other.vertices[i].color)
	return 1;
    }
  /* Compare vertex degrees */
  remove_duplicate_edges();
  other.remove_duplicate_edges();
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      if(vertices[i].nof_edges() < other.vertices[i].nof_edges())
	return -1;
      if(vertices[i].nof_edges() > other.vertices[i].nof_edges())
	return 1;
    }
  /* Compare edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v1 = vertices[i];
      Vertex &v2 = other.vertices[i];
      v1.sort_edges();
      v2.sort_edges();
      std::vector<unsigned int>::const_iterator ei1 = v1.edges.begin();
      std::vector<unsigned int>::const_iterator ei2 = v2.edges.begin();
      while(ei1 != v1.edges.end())
	{
	  if(*ei1 < *ei2)
	    return -1;
	  if(*ei1 > *ei2)
	    return 1;
	  ei1++;
	  ei2++;
	}
    }
  return 0;
}


Graph*
Graph::permute(const std::vector<unsigned int>& perm) const
{
#if defined(BLISS_CONSISTENCY_CHECKS)
#endif

  Graph* const g = new Graph(get_nof_vertices());
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex& v = vertices[i];
      Vertex& permuted_v = g->vertices[perm[i]];
      permuted_v.color = v.color;
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int dest_v = *ei;
	  permuted_v.add_edge(perm[dest_v]);
	}
      permuted_v.sort_edges();
    }
  return g;
}

Graph*
Graph::permute(const unsigned int* perm) const
{
#if defined(BLISS_CONSISTENCY_CHECKS)
  if(!is_permutation(get_nof_vertices(), perm))
    _INTERNAL_ERROR();
#endif

  Graph* const g = new Graph(get_nof_vertices());
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex& v = vertices[i];
      Vertex& permuted_v = g->vertices[perm[i]];
      permuted_v.color = v.color;
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int dest_v = *ei;
	  permuted_v.add_edge(perm[dest_v]);
	}
      permuted_v.sort_edges();
    }
  return g;
}


/*-------------------------------------------------------------------------
 *
 * Print graph in graphviz format
 *
 *-------------------------------------------------------------------------*/


#if 0
void
Graph::write_dot(const char* const filename)
{
  FILE *fp = fopen(filename, "w");
  if(fp)
    {
      write_dot(fp);
      fclose(fp);
    }
}

void
Graph::write_dot(FILE* const fp)
{
  remove_duplicate_edges();

  fprintf(fp, "graph g {\n");

  unsigned int vnum = 0;
  for(std::vector<Vertex>::iterator vi = vertices.begin();
      vi != vertices.end();
      vi++, vnum++)
    {
      Vertex& v = *vi;
      fprintf(fp, "v%u [label=\"%u:%u\"];\n", vnum, vnum, v.color);
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int vnum2 = *ei;
	  if(vnum2 > vnum)
	    fprintf(fp, "v%u -- v%u\n", vnum, vnum2);
	}
    }

  fprintf(fp, "}\n");
}
#endif


/*-------------------------------------------------------------------------
 *
 * Get a hash value for the graph.
 *
 *-------------------------------------------------------------------------*/

unsigned int
Graph::get_hash()
{
  remove_duplicate_edges();
  sort_edges();

  UintSeqHash h;

  h.update(get_nof_vertices());

  /* Hash the color of each vertex */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      h.update(vertices[i].color);
    }

  /* Hash the edges */
  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex &v = vertices[i];
      for(std::vector<unsigned int>::const_iterator ei = v.edges.begin();
	  ei != v.edges.end();
	  ei++)
	{
	  const unsigned int dest_i = *ei;
	  if(dest_i < i)
	    continue;
	  h.update(i);
	  h.update(dest_i);
	}
    }

  return h.get_value();
}


void
Graph::remove_duplicate_edges()
{
  std::vector<bool> tmp(vertices.size(), false);

  for(std::vector<Vertex>::iterator vi = vertices.begin();
      vi != vertices.end();
      vi++)
    {
#if defined(BLISS_EXPENSIVE_CONSISTENCY_CHECKS)
      for(unsigned int i = 0; i < tmp.size(); i++) assert(tmp[i] == false);
#endif
      (*vi).remove_duplicate_edges(tmp);
    }
}


/*-------------------------------------------------------------------------
 *
 * Partition independent invariants
 *
 *-------------------------------------------------------------------------*/

/*
 * Return the color of the vertex.
 * Time complexity: O(1)
 */
unsigned int
Graph::vertex_color_invariant(const Graph* const g, const unsigned int v)
{
  return g->vertices[v].color;
}

/*
 * Return the degree of the vertex.
 * Time complexity: O(1)
 */
unsigned int
Graph::degree_invariant(const Graph* const g, const unsigned int v)
{
  return g->vertices[v].nof_edges();
}

/*
 * Return 1 if the vertex v has a self-loop, 0 otherwise
 * Time complexity: O(E_v), where E_v is the number of edges leaving v
 */
unsigned int
Graph::selfloop_invariant(const Graph* const g, const unsigned int v)
{
  const Vertex& vertex = g->vertices[v];
  for(std::vector<unsigned int>::const_iterator ei = vertex.edges.begin();
      ei != vertex.edges.end();
      ei++)
    {
      if(*ei == v)
	return 1;
    }
  return 0;
}


/*-------------------------------------------------------------------------
 *
 * Refine the partition p according to a partition independent invariant
 *
 *-------------------------------------------------------------------------*/

bool
Graph::refine_according_to_invariant(unsigned int (*inv)(const Graph* const g,
							 const unsigned int v))
{
  bool refined = false;

  for(Partition::Cell* cell = p.first_nonsingleton_cell; cell; )
    {

      Partition::Cell* const next_cell = cell->next_nonsingleton;

      const unsigned int* ep = p.elements + cell->first;
      for(unsigned int i = cell->length; i > 0; i--, ep++)
	{
	  const unsigned int ival = inv(this, *ep);
	  p.invariant_values[*ep] = ival;
	  if(ival > cell->max_ival)
	    {
	      cell->max_ival = ival;
	      cell->max_ival_count = 1;
	    }
	  else if(ival == cell->max_ival)
	    {
	      cell->max_ival_count++;
	    }
	}
      Partition::Cell* const last_new_cell = p.zplit_cell(cell, true);
      refined |= (last_new_cell != cell);
      cell = next_cell;
    }

  return refined;
}


/*-------------------------------------------------------------------------
 *
 * Split the neighbourhood of a cell according to the equitable invariant
 *
 *-------------------------------------------------------------------------*/

bool
Graph::split_neighbourhood_of_cell(Partition::Cell* const cell)
{


  const bool was_equal_to_first = refine_equal_to_first;

  if(compute_eqref_hash)
    {
      eqref_hash.update(cell->first);
      eqref_hash.update(cell->length);
    }

  const unsigned int* ep = p.elements + cell->first;
  for(unsigned int i = cell->length; i > 0; i--)
    {
      const Vertex& v = vertices[*ep++];

      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j != 0; j--)
	{
	  const unsigned int dest_vertex = *ei++;
	  Partition::Cell * const neighbour_cell = p.get_cell(dest_vertex);
	  if(neighbour_cell->is_unit())
	    continue;
	  const unsigned int ival = ++p.invariant_values[dest_vertex];
	  if(ival > neighbour_cell->max_ival)
	    {
	      neighbour_cell->max_ival = ival;
	      neighbour_cell->max_ival_count = 1;
	      if(ival == 1) {
		neighbour_heap.insert(neighbour_cell->first);
	      }
	    }
	  else if(ival == neighbour_cell->max_ival) {
	    neighbour_cell->max_ival_count++;
	  }
	}
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell * const neighbour_cell = p.get_cell(p.elements[start]);

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}


      Partition::Cell* const last_new_cell = p.zplit_cell(neighbour_cell, true);

      /* Update certificate and hash if needed */
      const Partition::Cell* c = neighbour_cell;
      while(1)
	{
	  if(in_search)
	    {
	      /* Build certificate */
	      cert_add_redundant(CERT_SPLIT, c->first, c->length);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	  if(compute_eqref_hash)
	    {
	      eqref_hash.update(c->first);
	      eqref_hash.update(c->length);
	    }
	  if(c == last_new_cell)
	    break;
	  c = c->next;
	}
    }

  if(refine_compare_certificate and
     (refine_equal_to_first == false) and
     (refine_cmp_to_best < 0))
    return true;

  return false;

 worse_exit:
  /* Clear neighbour heap */
  UintSeqHash rest;
  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell * const neighbour_cell = p.get_cell(p.elements[start]);
      if(opt_use_failure_recording and was_equal_to_first)
	{
	  rest.update(neighbour_cell->first);
	  rest.update(neighbour_cell->length);
	  rest.update(neighbour_cell->max_ival);
	  rest.update(neighbour_cell->max_ival_count);
	}
      neighbour_cell->max_ival = 0;
      neighbour_cell->max_ival_count = 0;
     p.clear_ivs(neighbour_cell);
    }
  if(opt_use_failure_recording and was_equal_to_first)
    {
      for(unsigned int i = p.splitting_queue.size(); i > 0; i--)
	{
	  Partition::Cell* const cell = p.splitting_queue.pop_front();
	  rest.update(cell->first);
	  rest.update(cell->length);
	  p.splitting_queue.push_back(cell);
	}
      rest.update(failure_recording_fp_deviation);
      failure_recording_fp_deviation = rest.get_value();
    }

  return true;
}


bool
Graph::split_neighbourhood_of_unit_cell(Partition::Cell* const unit_cell)
{


  const bool was_equal_to_first = refine_equal_to_first;

  if(compute_eqref_hash)
    {
      eqref_hash.update(0x87654321);
      eqref_hash.update(unit_cell->first);
      eqref_hash.update(1);
    }

  const Vertex& v = vertices[p.elements[unit_cell->first]];

  std::vector<unsigned int>::const_iterator ei = v.edges.begin();
  for(unsigned int j = v.nof_edges(); j > 0; j--)
    {
      const unsigned int dest_vertex = *ei++;
      Partition::Cell * const neighbour_cell = p.get_cell(dest_vertex);

      if(neighbour_cell->is_unit()) {
	if(in_search) {
	  /* Remember neighbour in order to generate certificate */
	  neighbour_heap.insert(neighbour_cell->first);
	}
	continue;
      }
      if(neighbour_cell->max_ival_count == 0)
	{
	  neighbour_heap.insert(neighbour_cell->first);
	}
      neighbour_cell->max_ival_count++;

      unsigned int * const swap_position =
	p.elements + neighbour_cell->first + neighbour_cell->length -
	neighbour_cell->max_ival_count;
      *p.in_pos[dest_vertex] = *swap_position;
      p.in_pos[*swap_position] = p.in_pos[dest_vertex];
      *swap_position = dest_vertex;
      p.in_pos[dest_vertex] = swap_position;
    }

  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell* neighbour_cell =	p.get_cell(p.elements[start]);

#if defined(BLISS_CONSISTENCY_CHECKS)
      if(neighbour_cell->is_unit()) {
      } else {
      }
#endif

      if(compute_eqref_hash)
	{
	  eqref_hash.update(neighbour_cell->first);
	  eqref_hash.update(neighbour_cell->length);
	  eqref_hash.update(neighbour_cell->max_ival_count);
	}

      if(neighbour_cell->length > 1 and
	 neighbour_cell->max_ival_count != neighbour_cell->length)
	{
	  Partition::Cell * const new_cell =
	    p.aux_split_in_two(neighbour_cell,
			       neighbour_cell->length -
			       neighbour_cell->max_ival_count);
	  unsigned int *ep = p.elements + new_cell->first;
	  unsigned int * const lp = p.elements+new_cell->first+new_cell->length;
	  while(ep < lp)
	    {
	      p.element_to_cell_map[*ep] = new_cell;
	      ep++;
	    }
	  neighbour_cell->max_ival_count = 0;


	  if(compute_eqref_hash)
	    {
	      /* Update hash */
	      eqref_hash.update(neighbour_cell->first);
	      eqref_hash.update(neighbour_cell->length);
	      eqref_hash.update(0);
	      eqref_hash.update(new_cell->first);
	      eqref_hash.update(new_cell->length);
	      eqref_hash.update(1);
	    }

	  /* Add cells in splitting_queue */
	  if(neighbour_cell->is_in_splitting_queue()) {
	    /* Both cells must be included in splitting_queue in order
	       to ensure refinement into equitable partition */
	    p.splitting_queue_add(new_cell);
	  } else {
	    Partition::Cell *min_cell, *max_cell;
	    if(neighbour_cell->length <= new_cell->length) {
	      min_cell = neighbour_cell;
	      max_cell = new_cell;
	    } else {
	      min_cell = new_cell;
	      max_cell = neighbour_cell;
	    }
	    /* Put the smaller cell in splitting_queue */
	    p.splitting_queue_add(min_cell);
	    if(max_cell->is_unit()) {
	      /* Put the "larger" cell also in splitting_queue */
	      p.splitting_queue_add(max_cell);
	    }
	  }
	  /* Update pointer for certificate generation */
	  neighbour_cell = new_cell;
	}
      else
	{
	  /* neighbour_cell->length == 1 ||
	     neighbour_cell->max_ival_count == neighbour_cell->length */
	  neighbour_cell->max_ival_count = 0;
	}

      /*
       * Build certificate if required
       */
      if(in_search)
	{
	  for(unsigned int i = neighbour_cell->first,
		j = neighbour_cell->length;
	      j > 0;
	      j--, i++)
	    {
	      /* Build certificate */
	      cert_add(CERT_EDGE, unit_cell->first, i);
	      /* No need to continue? */
	      if(refine_compare_certificate and
		 (refine_equal_to_first == false) and
		 (refine_cmp_to_best < 0))
		goto worse_exit;
	    }
	} /* if(in_search) */
    } /* while(!neighbour_heap.is_empty()) */

  if(refine_compare_certificate and
     (refine_equal_to_first == false) and
     (refine_cmp_to_best < 0))
    return true;

  return false;

 worse_exit:
  /* Clear neighbour heap */
  UintSeqHash rest;
  while(!neighbour_heap.is_empty())
    {
      const unsigned int start = neighbour_heap.remove();
      Partition::Cell * const neighbour_cell = p.get_cell(p.elements[start]);
      if(opt_use_failure_recording and was_equal_to_first)
	{
	  rest.update(neighbour_cell->first);
	  rest.update(neighbour_cell->length);
	  rest.update(neighbour_cell->max_ival_count);
	}
      neighbour_cell->max_ival_count = 0;
    }
  if(opt_use_failure_recording and was_equal_to_first)
    {
      rest.update(failure_recording_fp_deviation);
      failure_recording_fp_deviation = rest.get_value();
    }
  return true;
}


/*-------------------------------------------------------------------------
 *
 * Check whether the current partition p is equitable.
 * Performance: very slow, use only for debugging purposes.
 *
 *-------------------------------------------------------------------------*/

bool Graph::is_equitable() const
{
  const unsigned int N = get_nof_vertices();
  if(N == 0)
    return true;

  std::vector<unsigned int> first_count = std::vector<unsigned int>(N, 0);
  std::vector<unsigned int> other_count = std::vector<unsigned int>(N, 0);

  for(Partition::Cell *cell = p.first_cell; cell; cell = cell->next)
    {
      if(cell->is_unit())
	continue;

      unsigned int *ep = p.elements + cell->first;
      const Vertex &first_vertex = vertices[*ep++];

      /* Count how many edges lead from the first vertex to
       * the neighbouring cells */
      for(std::vector<unsigned int>::const_iterator ei =
	    first_vertex.edges.begin();
	  ei != first_vertex.edges.end();
	  ei++)
	{
	  first_count[p.get_cell(*ei)->first]++;
	}

      /* Count and compare to the edges of the other vertices */
      for(unsigned int i = cell->length; i > 1; i--)
	{
	  const Vertex &vertex = vertices[*ep++];
	  for(std::vector<unsigned int>::const_iterator ei =
		vertex.edges.begin();
	      ei != vertex.edges.end();
	      ei++)
	    {
	      other_count[p.get_cell(*ei)->first]++;
	    }
	  for(Partition::Cell *cell2 = p.first_cell;
	      cell2;
	      cell2 = cell2->next)
	    {
	      if(first_count[cell2->first] != other_count[cell2->first])
		{
		  /* Not equitable */
		  return false;
		}
	      other_count[cell2->first] = 0;
	    }
	}
      /* Reset first_count */
      for(unsigned int i = 0; i < N; i++)
	first_count[i] = 0;
    }
  return true;
}


/*-------------------------------------------------------------------------
 *
 * Build the initial equitable partition
 *
 *-------------------------------------------------------------------------*/

void Graph::make_initial_equitable_partition()
{
  refine_according_to_invariant(&vertex_color_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_according_to_invariant(&selfloop_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_according_to_invariant(&degree_invariant);
  p.splitting_queue_clear();
  //p.print_signature(stderr); fprintf(stderr, "\n");

  refine_to_equitable();
  //p.print_signature(stderr); fprintf(stderr, "\n");

}


/*-------------------------------------------------------------------------
 *
 * Find the next cell to be splitted
 *
 *-------------------------------------------------------------------------*/


Partition::Cell*
Graph::find_next_cell_to_be_splitted(Partition::Cell* cell)
{
  switch(sh) {
  case shs_f:   return sh_first();
  case shs_fs:  return sh_first_smallest();
  case shs_fl:  return sh_first_largest();
  case shs_fm:  return sh_first_max_neighbours();
  case shs_fsm: return sh_first_smallest_max_neighbours();
  case shs_flm: return sh_first_largest_max_neighbours();
  default:
    fatal_error("Internal error - unknown splitting heuristics");
    return 0;
  }
}

/** \internal
 * A splitting heuristic.
 * Returns the first nonsingleton cell in the current partition.
 */
Partition::Cell*
Graph::sh_first()
{
  Partition::Cell* best_cell = 0;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      best_cell = cell;
      break;
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first smallest nonsingleton cell in the current partition.
 */
Partition::Cell*
Graph::sh_first_smallest()
{
  Partition::Cell* best_cell = 0;
  unsigned int best_size = UINT_MAX;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      if(cell->length < best_size)
	{
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first largest nonsingleton cell in the current partition.
 */
Partition::Cell*
Graph::sh_first_largest()
{
  Partition::Cell* best_cell = 0;
  unsigned int best_size = 0;
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      if(cell->length > best_size)
	{
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first nonsingleton cell with max number of neighbouring
 *   nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Graph::sh_first_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {
      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j > 0; j--)
	{
	  Partition::Cell * const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      int value = 0;
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}
      if(value > best_value)
	{
	  best_value = value;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first smallest nonsingleton cell with max number of neighbouring
 * nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Graph::sh_first_smallest_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  unsigned int best_size = UINT_MAX;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {

      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;

      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j > 0; j--)
	{
	  Partition::Cell* const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      int value = 0;
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}
      if((value > best_value) or
	 (value == best_value and cell->length < best_size))
	{
	  best_value = value;
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}

/** \internal
 * A splitting heuristic.
 * Returns the first largest nonsingleton cell with max number of neighbouring
 * nonsingleton cells.
 * Assumes that the partition p is equitable.
 * Assumes that the max_ival fields of the cells are all 0.
 */
Partition::Cell*
Graph::sh_first_largest_max_neighbours()
{
  Partition::Cell* best_cell = 0;
  int best_value = -1;
  unsigned int best_size = 0;
  KStack<Partition::Cell*> neighbour_cells_visited;
  neighbour_cells_visited.init(get_nof_vertices());
  for(Partition::Cell* cell = p.first_nonsingleton_cell;
      cell;
      cell = cell->next_nonsingleton)
    {

      if(opt_use_comprec and p.cr_get_level(cell->first) != cr_level)
	continue;
      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j > 0; j--)
	{
	  Partition::Cell* const neighbour_cell = p.get_cell(*ei++);
	  if(neighbour_cell->is_unit())
	    continue;
	  neighbour_cell->max_ival++;
	  if(neighbour_cell->max_ival == 1)
	    neighbour_cells_visited.push(neighbour_cell);
	}
      int value = 0;
      while(!neighbour_cells_visited.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbour_cells_visited.pop();
	  if(neighbour_cell->max_ival != neighbour_cell->length)
	    value++;
	  neighbour_cell->max_ival = 0;
	}
      if((value > best_value) or
	 (value == best_value and cell->length > best_size))
	{
	  best_value = value;
	  best_size = cell->length;
	  best_cell = cell;
	}
    }
  return best_cell;
}


/*-------------------------------------------------------------------------
 *
 * Initialize the certificate size and memory
 *
 *-------------------------------------------------------------------------*/

void
Graph::initialize_certificate()
{
  certificate_index = 0;
  certificate_current_path.clear();
  certificate_first_path.clear();
  certificate_best_path.clear();
}


/*-------------------------------------------------------------------------
 *
 * Check whether perm is an automorphism.
 * Slow, mainly for debugging and validation purposes.
 *
 *-------------------------------------------------------------------------*/

bool
Graph::is_automorphism(unsigned int* const perm)
{
  std::set<unsigned int, std::less<unsigned int> > edges1;
  std::set<unsigned int, std::less<unsigned int> > edges2;

#if defined(BLISS_CONSISTENCY_CHECKS)
  if(!is_permutation(get_nof_vertices(), perm))
    _INTERNAL_ERROR();
#endif

  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      Vertex& v1 = vertices[i];
      edges1.clear();
      for(std::vector<unsigned int>::iterator ei = v1.edges.begin();
	  ei != v1.edges.end();
	  ei++)
	edges1.insert(perm[*ei]);

      Vertex& v2 = vertices[perm[i]];
      edges2.clear();
      for(std::vector<unsigned int>::iterator ei = v2.edges.begin();
	  ei != v2.edges.end();
	  ei++)
	edges2.insert(*ei);

      if(!(edges1 == edges2))
	return false;
    }

  return true;
}


bool
Graph::is_automorphism(const std::vector<unsigned int>& perm) const
{

  if(!(perm.size() == get_nof_vertices() and is_permutation(perm)))
    return false;

  std::set<unsigned int, std::less<unsigned int> > edges1;
  std::set<unsigned int, std::less<unsigned int> > edges2;

  for(unsigned int i = 0; i < get_nof_vertices(); i++)
    {
      const Vertex& v1 = vertices[i];
      edges1.clear();
      for(std::vector<unsigned int>::const_iterator ei = v1.edges.begin();
	  ei != v1.edges.end();
	  ei++)
	edges1.insert(perm[*ei]);

      const Vertex& v2 = vertices[perm[i]];
      edges2.clear();
      for(std::vector<unsigned int>::const_iterator ei = v2.edges.begin();
	  ei != v2.edges.end();
	  ei++)
	edges2.insert(*ei);

      if(!(edges1 == edges2))
	return false;
    }

  return true;
}


bool
Graph::nucr_find_first_component(const unsigned int level)
{

  cr_component.clear();
  cr_component_elements = 0;

  /* Find first non-discrete cell in the component level */
  Partition::Cell* first_cell = p.first_nonsingleton_cell;
  while(first_cell)
    {
      if(p.cr_get_level(first_cell->first) == level)
	break;
      first_cell = first_cell->next_nonsingleton;
    }

  /* The component is discrete, return false */
  if(!first_cell)
    return false;

  std::vector<Partition::Cell*> component;
  first_cell->max_ival = 1;
  component.push_back(first_cell);

  for(unsigned int i = 0; i < component.size(); i++)
    {
      Partition::Cell* const cell = component[i];

      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;

	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);

	  /* Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Already marked to be in the same component? */
	  if(neighbour_cell->max_ival == 1)
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  if(p.cr_get_level(neighbour_cell->first) != level)
	    continue;

	  if(neighbour_cell->max_ival_count == 0)
	    neighbour_heap.insert(neighbour_cell->first);
	  neighbour_cell->max_ival_count++;
	}
      while(!neighbour_heap.is_empty())
	{
	  const unsigned int start = neighbour_heap.remove();
	  Partition::Cell* const neighbour_cell =
	    p.get_cell(p.elements[start]);

	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  neighbour_cell->max_ival_count = 0;
	  neighbour_cell->max_ival = 1;
	  component.push_back(neighbour_cell);
	}
    }

  for(unsigned int i = 0; i < component.size(); i++)
    {
      Partition::Cell* const cell = component[i];
      cell->max_ival = 0;
      cr_component.push_back(cell->first);
      cr_component_elements += cell->length;
    }

  return true;
}


bool
Graph::nucr_find_first_component(const unsigned int level,
				 std::vector<unsigned int>& component,
				 unsigned int& component_elements,
				 Partition::Cell*& sh_return)
{

  component.clear();
  component_elements = 0;
  sh_return = 0;
  unsigned int sh_first  = 0;
  unsigned int sh_size   = 0;
  unsigned int sh_nuconn = 0;

  /* Find first non-discrete cell in the component level */
  Partition::Cell* first_cell = p.first_nonsingleton_cell;
  while(first_cell)
    {
      if(p.cr_get_level(first_cell->first) == level)
	break;
      first_cell = first_cell->next_nonsingleton;
    }

  if(!first_cell)
    {
      /* The component is discrete, return false */
      return false;
    }

  std::vector<Partition::Cell*> comp;
  KStack<Partition::Cell*> neighbours;
  neighbours.init(get_nof_vertices());

  first_cell->max_ival = 1;
  comp.push_back(first_cell);

  for(unsigned int i = 0; i < comp.size(); i++)
    {
      Partition::Cell* const cell = comp[i];

      const Vertex& v = vertices[p.elements[cell->first]];
      std::vector<unsigned int>::const_iterator ei = v.edges.begin();
      for(unsigned int j = v.nof_edges(); j > 0; j--)
	{
	  const unsigned int neighbour = *ei++;

	  Partition::Cell* const neighbour_cell = p.get_cell(neighbour);

	  /* Skip unit neighbours */
	  if(neighbour_cell->is_unit())
	    continue;
	  /* Is the neighbour at the same component recursion level? */
	  //if(p.cr_get_level(neighbour_cell->first) != level)
	  //  continue;
	  if(neighbour_cell->max_ival_count == 0)
	    neighbours.push(neighbour_cell);
	  neighbour_cell->max_ival_count++;
	}
      unsigned int nuconn = 1;
      while(!neighbours.is_empty())
	{
	  Partition::Cell* const neighbour_cell = neighbours.pop();
	  //neighbours.pop_back();

	  /* Skip saturated neighbour cells */
	  if(neighbour_cell->max_ival_count == neighbour_cell->length)
	    {
	      neighbour_cell->max_ival_count = 0;
	      continue;
	    }
	  nuconn++;
	  neighbour_cell->max_ival_count = 0;
	  if(neighbour_cell->max_ival == 0) {
	    comp.push_back(neighbour_cell);
	    neighbour_cell->max_ival = 1;
	  }
	}

      switch(sh) {
      case shs_f:
	if(sh_return == 0 or
	   cell->first <= sh_first) {
	  sh_return = cell;
	  sh_first = cell->first;
	}
	break;
      case shs_fs:
	if(sh_return == 0 or
	   cell->length < sh_size or
	   (cell->length == sh_size and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	}
	break;
      case shs_fl:
	if(sh_return == 0 or
	   cell->length > sh_size or
	   (cell->length == sh_size and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	}
	break;
      case shs_fm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and cell->first <= sh_first)) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_nuconn = nuconn;
	}
	break;
      case shs_fsm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and
	    (cell->length < sh_size or
	     (cell->length == sh_size and cell->first <= sh_first)))) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	  sh_nuconn = nuconn;
	}
	break;
      case shs_flm:
	if(sh_return == 0 or
	   nuconn > sh_nuconn or
	   (nuconn == sh_nuconn and
	    (cell->length > sh_size or
	     (cell->length == sh_size and cell->first <= sh_first)))) {
	  sh_return = cell;
	  sh_first = cell->first;
	  sh_size = cell->length;
	  sh_nuconn = nuconn;
	}
	break;
      default:
	fatal_error("Internal error - unknown splitting heuristics");
	return 0;
      }
    }
  assert(sh_return);

  for(unsigned int i = 0; i < comp.size(); i++)
    {
      Partition::Cell* const cell = comp[i];
      cell->max_ival = 0;
      component.push_back(cell->first);
      component_elements += cell->length;
    }

  return true;
}


}