1 // Copyright Daniel Trebbien 2010. 2 // Distributed under the Boost Software License, Version 1.0. 3 // (See accompanying file LICENSE_1_0.txt or the copy at 4 // http://www.boost.org/LICENSE_1_0.txt) 5 6 #ifndef BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP 7 #define BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP 1 8 9 #include <boost/assert.hpp> 10 #include <set> 11 #include <vector> 12 #include <boost/concept_check.hpp> 13 #include <boost/concept/assert.hpp> 14 #include <boost/graph/adjacency_list.hpp> 15 #include <boost/graph/buffer_concepts.hpp> 16 #include <boost/graph/exception.hpp> 17 #include <boost/graph/graph_traits.hpp> 18 #include <boost/graph/maximum_adjacency_search.hpp> 19 #include <boost/graph/named_function_params.hpp> 20 #include <boost/graph/one_bit_color_map.hpp> 21 #include <boost/graph/detail/d_ary_heap.hpp> 22 #include <boost/property_map/property_map.hpp> 23 #include <boost/tuple/tuple.hpp> 24 #include <boost/utility/result_of.hpp> 25 #include <boost/graph/iteration_macros.hpp> 26 27 namespace boost { 28 29 namespace detail { 30 template < typename ParityMap, typename WeightMap, typename IndexMap > 31 class mas_min_cut_visitor : public boost::default_mas_visitor { 32 typedef one_bit_color_map <IndexMap> InternalParityMap; 33 typedef typename boost::property_traits<WeightMap>::value_type weight_type; 34 public: 35 template < typename Graph > mas_min_cut_visitor(const Graph & g,ParityMap parity,weight_type & cutweight,const WeightMap & weight_map,IndexMap index_map)36 mas_min_cut_visitor(const Graph& g, 37 ParityMap parity, 38 weight_type& cutweight, 39 const WeightMap& weight_map, 40 IndexMap index_map) 41 : m_bestParity(parity), 42 m_parity(make_one_bit_color_map(num_vertices(g), index_map)), 43 m_bestWeight(cutweight), 44 m_cutweight(0), 45 m_visited(0), 46 m_weightMap(weight_map) 47 { 48 // set here since the init list sets the reference 49 m_bestWeight = (std::numeric_limits<weight_type>::max)(); 50 } 51 52 template < typename Vertex, typename Graph > initialize_vertex(Vertex u,const Graph & g)53 void initialize_vertex(Vertex u, const Graph & g) 54 { 55 typedef typename boost::property_traits<ParityMap>::value_type parity_type; 56 typedef typename boost::property_traits<InternalParityMap>::value_type internal_parity_type; 57 58 put(m_parity, u, internal_parity_type(0)); 59 put(m_bestParity, u, parity_type(0)); 60 } 61 62 template < typename Edge, typename Graph > examine_edge(Edge e,const Graph & g)63 void examine_edge(Edge e, const Graph & g) 64 { 65 weight_type w = get(m_weightMap, e); 66 67 // if the target of e is already marked then decrease cutweight 68 // otherwise, increase it 69 if (get(m_parity, boost::target(e, g))) { 70 m_cutweight -= w; 71 } else { 72 m_cutweight += w; 73 } 74 } 75 76 template < typename Vertex, typename Graph > finish_vertex(Vertex u,const Graph & g)77 void finish_vertex(Vertex u, const Graph & g) 78 { 79 typedef typename boost::property_traits<InternalParityMap>::value_type internal_parity_type; 80 81 ++m_visited; 82 put(m_parity, u, internal_parity_type(1)); 83 84 if (m_cutweight < m_bestWeight && m_visited < num_vertices(g)) { 85 m_bestWeight = m_cutweight; 86 BGL_FORALL_VERTICES_T(i, g, Graph) { 87 put(m_bestParity,i, get(m_parity,i)); 88 } 89 } 90 } 91 clear()92 inline void clear() { 93 m_bestWeight = (std::numeric_limits<weight_type>::max)(); 94 m_visited = 0; 95 m_cutweight = 0; 96 } 97 98 private: 99 ParityMap m_bestParity; 100 InternalParityMap m_parity; 101 weight_type& m_bestWeight; 102 weight_type m_cutweight; 103 unsigned m_visited; 104 const WeightMap& m_weightMap; 105 }; 106 107 /** 108 * \brief Computes a min-cut of the input graph 109 * 110 * Computes a min-cut of the input graph using the Stoer-Wagner algorithm. 111 * 112 * \pre \p g is a connected, undirected graph 113 * \pre <code>pq.empty()</code> 114 * \param[in] g the input graph 115 * \param[in] weights a readable property map from each edge to its weight (a non-negative value) 116 * \param[out] parities a writable property map from each vertex to a bool type object for 117 * distinguishing the two vertex sets of the min-cut 118 * \param[out] assignments a read/write property map from each vertex to a \c vertex_descriptor object. This 119 * map serves as work space, and no particular meaning should be derived from property values 120 * after completion of the algorithm. 121 * \param[out] pq a keyed, updatable max-priority queue 122 * \returns the cut weight of the min-cut 123 * \see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.114.6687&rep=rep1&type=pdf 124 * \see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.614&rep=rep1&type=pdf 125 * 126 * \author Daniel Trebbien 127 * \date 2010-09-11 128 */ 129 template <class UndirectedGraph, class WeightMap, class ParityMap, class VertexAssignmentMap, class KeyedUpdatablePriorityQueue, class IndexMap> 130 typename boost::property_traits<WeightMap>::value_type stoer_wagner_min_cut(const UndirectedGraph & g,WeightMap weights,ParityMap parities,VertexAssignmentMap assignments,KeyedUpdatablePriorityQueue & pq,IndexMap index_map)131 stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights, ParityMap parities, VertexAssignmentMap assignments, KeyedUpdatablePriorityQueue& pq, IndexMap index_map) { 132 typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor; 133 typedef typename boost::property_traits<WeightMap>::value_type weight_type; 134 135 typename graph_traits<UndirectedGraph>::vertex_iterator u_iter, u_end; 136 137 weight_type bestW = (std::numeric_limits<weight_type>::max)(); 138 weight_type bestThisTime = (std::numeric_limits<weight_type>::max)(); 139 vertex_descriptor bestStart = boost::graph_traits<UndirectedGraph>::null_vertex(); 140 141 detail::mas_min_cut_visitor<ParityMap, WeightMap, IndexMap> 142 vis(g, parities, bestThisTime, weights, index_map); 143 144 // for each node in the graph, 145 for (boost::tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter) { 146 // run the MAS and find the min cut 147 vis.clear(); 148 boost::maximum_adjacency_search(g, 149 boost::weight_map(weights). 150 visitor(vis). 151 root_vertex(*u_iter). 152 vertex_assignment_map(assignments). 153 max_priority_queue(pq)); 154 if (bestThisTime < bestW) { 155 bestW = bestThisTime; 156 bestStart = *u_iter; 157 } 158 } 159 160 // Run one more time, starting from the best start location, to 161 // ensure the visitor has the best values. 162 vis.clear(); 163 boost::maximum_adjacency_search(g, 164 boost::vertex_assignment_map(assignments). 165 weight_map(weights). 166 visitor(vis). 167 root_vertex(bestStart). 168 max_priority_queue(pq)); 169 170 return bestW; 171 } 172 } // end `namespace detail` within `namespace boost` 173 174 template <class UndirectedGraph, class WeightMap, class ParityMap, class VertexAssignmentMap, class KeyedUpdatablePriorityQueue, class IndexMap> 175 typename boost::property_traits<WeightMap>::value_type stoer_wagner_min_cut(const UndirectedGraph & g,WeightMap weights,ParityMap parities,VertexAssignmentMap assignments,KeyedUpdatablePriorityQueue & pq,IndexMap index_map)176 stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights, ParityMap parities, VertexAssignmentMap assignments, KeyedUpdatablePriorityQueue& pq, IndexMap index_map) { 177 BOOST_CONCEPT_ASSERT((boost::IncidenceGraphConcept<UndirectedGraph>)); 178 BOOST_CONCEPT_ASSERT((boost::VertexListGraphConcept<UndirectedGraph>)); 179 typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor; 180 typedef typename boost::graph_traits<UndirectedGraph>::vertices_size_type vertices_size_type; 181 typedef typename boost::graph_traits<UndirectedGraph>::edge_descriptor edge_descriptor; 182 BOOST_CONCEPT_ASSERT((boost::Convertible<typename boost::graph_traits<UndirectedGraph>::directed_category, boost::undirected_tag>)); 183 BOOST_CONCEPT_ASSERT((boost::ReadablePropertyMapConcept<WeightMap, edge_descriptor>)); 184 // typedef typename boost::property_traits<WeightMap>::value_type weight_type; 185 BOOST_CONCEPT_ASSERT((boost::WritablePropertyMapConcept<ParityMap, vertex_descriptor>)); 186 // typedef typename boost::property_traits<ParityMap>::value_type parity_type; 187 BOOST_CONCEPT_ASSERT((boost::ReadWritePropertyMapConcept<VertexAssignmentMap, vertex_descriptor>)); 188 BOOST_CONCEPT_ASSERT((boost::Convertible<vertex_descriptor, typename boost::property_traits<VertexAssignmentMap>::value_type>)); 189 BOOST_CONCEPT_ASSERT((boost::KeyedUpdatableQueueConcept<KeyedUpdatablePriorityQueue>)); 190 191 vertices_size_type n = num_vertices(g); 192 if (n < 2) 193 throw boost::bad_graph("the input graph must have at least two vertices."); 194 else if (!pq.empty()) 195 throw std::invalid_argument("the max-priority queue must be empty initially."); 196 197 return detail::stoer_wagner_min_cut(g, weights, 198 parities, assignments, pq, index_map); 199 } 200 201 namespace graph { 202 namespace detail { 203 template <class UndirectedGraph, class WeightMap> 204 struct stoer_wagner_min_cut_impl { 205 typedef typename boost::property_traits<WeightMap>::value_type result_type; 206 template <typename ArgPack> operator ()boost::graph::detail::stoer_wagner_min_cut_impl207 result_type operator() (const UndirectedGraph& g, WeightMap weights, const ArgPack& arg_pack) const { 208 using namespace boost::graph::keywords; 209 typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor; 210 typedef typename boost::property_traits<WeightMap>::value_type weight_type; 211 212 typedef boost::detail::make_priority_queue_from_arg_pack_gen<boost::graph::keywords::tag::max_priority_queue, weight_type, vertex_descriptor, std::greater<weight_type> > gen_type; 213 214 gen_type gen(choose_param(get_param(arg_pack, boost::distance_zero_t()), weight_type(0))); 215 216 typename boost::result_of<gen_type(const UndirectedGraph&, const ArgPack&)>::type pq = gen(g, arg_pack); 217 218 boost::dummy_property_map dummy_prop; 219 return boost::stoer_wagner_min_cut(g, 220 weights, 221 arg_pack [_parity_map | dummy_prop], 222 boost::detail::make_property_map_from_arg_pack_gen<tag::vertex_assignment_map, vertex_descriptor>(vertex_descriptor())(g, arg_pack), 223 pq, 224 boost::detail::override_const_property(arg_pack, _vertex_index_map, g, vertex_index) 225 ); 226 } 227 }; 228 } 229 BOOST_GRAPH_MAKE_FORWARDING_FUNCTION(stoer_wagner_min_cut,2,4) 230 } 231 232 // Named parameter interface 233 BOOST_GRAPH_MAKE_OLD_STYLE_PARAMETER_FUNCTION(stoer_wagner_min_cut, 2) 234 namespace graph { 235 // version without IndexMap kept for backwards compatibility 236 // (but requires vertex_index_t to be defined in the graph) 237 // Place after the macro to avoid compilation errors 238 template <class UndirectedGraph, class WeightMap, class ParityMap, class VertexAssignmentMap, class KeyedUpdatablePriorityQueue> 239 typename boost::property_traits<WeightMap>::value_type stoer_wagner_min_cut(const UndirectedGraph & g,WeightMap weights,ParityMap parities,VertexAssignmentMap assignments,KeyedUpdatablePriorityQueue & pq)240 stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights, ParityMap parities, VertexAssignmentMap assignments, KeyedUpdatablePriorityQueue& pq) { 241 242 return stoer_wagner_min_cut(g, weights, 243 parities, assignments, pq, 244 get(vertex_index, g)); 245 } 246 } // end `namespace graph` 247 } // end `namespace boost` 248 249 #include <boost/graph/iteration_macros_undef.hpp> 250 251 #endif // !BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP 252