1 // 2 //======================================================================= 3 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame. 4 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek 5 // 6 // Distributed under the Boost Software License, Version 1.0. (See 7 // accompanying file LICENSE_1_0.txt or copy at 8 // http://www.boost.org/LICENSE_1_0.txt) 9 //======================================================================= 10 // 11 12 #ifndef BOOST_GRAPH_STRONG_COMPONENTS_HPP 13 #define BOOST_GRAPH_STRONG_COMPONENTS_HPP 14 15 #include <stack> 16 #include <boost/config.hpp> 17 #include <boost/graph/depth_first_search.hpp> 18 #include <boost/type_traits/conversion_traits.hpp> 19 #include <boost/static_assert.hpp> 20 #include <boost/graph/overloading.hpp> 21 #include <boost/graph/detail/mpi_include.hpp> 22 #include <boost/concept/assert.hpp> 23 24 namespace boost { 25 26 //========================================================================== 27 // This is Tarjan's algorithm for strongly connected components 28 // from his paper "Depth first search and linear graph algorithms". 29 // It calculates the components in a single application of DFS. 30 // We implement the algorithm as a dfs-visitor. 31 32 namespace detail { 33 34 template <typename ComponentMap, typename RootMap, typename DiscoverTime, 35 typename Stack> 36 class tarjan_scc_visitor : public dfs_visitor<> 37 { 38 typedef typename property_traits<ComponentMap>::value_type comp_type; 39 typedef typename property_traits<DiscoverTime>::value_type time_type; 40 public: tarjan_scc_visitor(ComponentMap comp_map,RootMap r,DiscoverTime d,comp_type & c_,Stack & s_)41 tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, 42 comp_type& c_, Stack& s_) 43 : c(c_), comp(comp_map), root(r), discover_time(d), 44 dfs_time(time_type()), s(s_) { } 45 46 template <typename Graph> discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,const Graph &)47 void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v, 48 const Graph&) { 49 put(root, v, v); 50 put(comp, v, (std::numeric_limits<comp_type>::max)()); 51 put(discover_time, v, dfs_time++); 52 s.push(v); 53 } 54 template <typename Graph> finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,const Graph & g)55 void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v, 56 const Graph& g) { 57 typename graph_traits<Graph>::vertex_descriptor w; 58 typename graph_traits<Graph>::out_edge_iterator ei, ei_end; 59 for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) { 60 w = target(*ei, g); 61 if (get(comp, w) == (std::numeric_limits<comp_type>::max)()) 62 put(root, v, this->min_discover_time(get(root,v), get(root,w))); 63 } 64 if (get(root, v) == v) { 65 do { 66 w = s.top(); s.pop(); 67 put(comp, w, c); 68 put(root, w, v); 69 } while (w != v); 70 ++c; 71 } 72 } 73 private: 74 template <typename Vertex> min_discover_time(Vertex u,Vertex v)75 Vertex min_discover_time(Vertex u, Vertex v) { 76 return get(discover_time, u) < get(discover_time,v) ? u : v; 77 } 78 79 comp_type& c; 80 ComponentMap comp; 81 RootMap root; 82 DiscoverTime discover_time; 83 time_type dfs_time; 84 Stack& s; 85 }; 86 87 template <class Graph, class ComponentMap, class RootMap, 88 class DiscoverTime, class P, class T, class R> 89 typename property_traits<ComponentMap>::value_type strong_components_impl(const Graph & g,ComponentMap comp,RootMap root,DiscoverTime discover_time,const bgl_named_params<P,T,R> & params)90 strong_components_impl 91 (const Graph& g, // Input 92 ComponentMap comp, // Output 93 // Internal record keeping 94 RootMap root, 95 DiscoverTime discover_time, 96 const bgl_named_params<P, T, R>& params) 97 { 98 typedef typename graph_traits<Graph>::vertex_descriptor Vertex; 99 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<ComponentMap, Vertex> )); 100 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<RootMap, Vertex> )); 101 typedef typename property_traits<RootMap>::value_type RootV; 102 BOOST_CONCEPT_ASSERT(( ConvertibleConcept<RootV, Vertex> )); 103 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<DiscoverTime, Vertex> )); 104 105 typename property_traits<ComponentMap>::value_type total = 0; 106 107 std::stack<Vertex> s; 108 detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime, 109 std::stack<Vertex> > 110 vis(comp, root, discover_time, total, s); 111 depth_first_search(g, params.visitor(vis)); 112 return total; 113 } 114 115 //------------------------------------------------------------------------- 116 // The dispatch functions handle the defaults for the rank and discover 117 // time property maps. 118 // dispatch with class specialization to avoid VC++ bug 119 120 template <class DiscoverTimeMap> 121 struct strong_comp_dispatch2 { 122 template <class Graph, class ComponentMap, class RootMap, class P, class T, class R> 123 inline static typename property_traits<ComponentMap>::value_type applyboost::detail::strong_comp_dispatch2124 apply(const Graph& g, 125 ComponentMap comp, 126 RootMap r_map, 127 const bgl_named_params<P, T, R>& params, 128 DiscoverTimeMap time_map) 129 { 130 return strong_components_impl(g, comp, r_map, time_map, params); 131 } 132 }; 133 134 135 template <> 136 struct strong_comp_dispatch2<param_not_found> { 137 template <class Graph, class ComponentMap, class RootMap, 138 class P, class T, class R> 139 inline static typename property_traits<ComponentMap>::value_type applyboost::detail::strong_comp_dispatch2140 apply(const Graph& g, 141 ComponentMap comp, 142 RootMap r_map, 143 const bgl_named_params<P, T, R>& params, 144 param_not_found) 145 { 146 typedef typename graph_traits<Graph>::vertices_size_type size_type; 147 size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1; 148 std::vector<size_type> time_vec(n); 149 return strong_components_impl 150 (g, comp, r_map, 151 make_iterator_property_map(time_vec.begin(), choose_const_pmap 152 (get_param(params, vertex_index), 153 g, vertex_index), time_vec[0]), 154 params); 155 } 156 }; 157 158 template <class Graph, class ComponentMap, class RootMap, 159 class P, class T, class R, class DiscoverTimeMap> 160 inline typename property_traits<ComponentMap>::value_type scc_helper2(const Graph & g,ComponentMap comp,RootMap r_map,const bgl_named_params<P,T,R> & params,DiscoverTimeMap time_map)161 scc_helper2(const Graph& g, 162 ComponentMap comp, 163 RootMap r_map, 164 const bgl_named_params<P, T, R>& params, 165 DiscoverTimeMap time_map) 166 { 167 return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map); 168 } 169 170 template <class RootMap> 171 struct strong_comp_dispatch1 { 172 173 template <class Graph, class ComponentMap, class P, class T, class R> 174 inline static typename property_traits<ComponentMap>::value_type applyboost::detail::strong_comp_dispatch1175 apply(const Graph& g, 176 ComponentMap comp, 177 const bgl_named_params<P, T, R>& params, 178 RootMap r_map) 179 { 180 return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time)); 181 } 182 }; 183 template <> 184 struct strong_comp_dispatch1<param_not_found> { 185 186 template <class Graph, class ComponentMap, 187 class P, class T, class R> 188 inline static typename property_traits<ComponentMap>::value_type applyboost::detail::strong_comp_dispatch1189 apply(const Graph& g, 190 ComponentMap comp, 191 const bgl_named_params<P, T, R>& params, 192 param_not_found) 193 { 194 typedef typename graph_traits<Graph>::vertex_descriptor Vertex; 195 typename std::vector<Vertex>::size_type 196 n = num_vertices(g) > 0 ? num_vertices(g) : 1; 197 std::vector<Vertex> root_vec(n); 198 return scc_helper2 199 (g, comp, 200 make_iterator_property_map(root_vec.begin(), choose_const_pmap 201 (get_param(params, vertex_index), 202 g, vertex_index), root_vec[0]), 203 params, 204 get_param(params, vertex_discover_time)); 205 } 206 }; 207 208 template <class Graph, class ComponentMap, class RootMap, 209 class P, class T, class R> 210 inline typename property_traits<ComponentMap>::value_type scc_helper1(const Graph & g,ComponentMap comp,const bgl_named_params<P,T,R> & params,RootMap r_map)211 scc_helper1(const Graph& g, 212 ComponentMap comp, 213 const bgl_named_params<P, T, R>& params, 214 RootMap r_map) 215 { 216 return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params, 217 r_map); 218 } 219 220 } // namespace detail 221 222 template <class Graph, class ComponentMap, 223 class P, class T, class R> 224 inline typename property_traits<ComponentMap>::value_type strong_components(const Graph & g,ComponentMap comp,const bgl_named_params<P,T,R> & params BOOST_GRAPH_ENABLE_IF_MODELS_PARM (Graph,vertex_list_graph_tag))225 strong_components(const Graph& g, ComponentMap comp, 226 const bgl_named_params<P, T, R>& params 227 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag)) 228 { 229 typedef typename graph_traits<Graph>::directed_category DirCat; 230 BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true)); 231 return detail::scc_helper1(g, comp, params, 232 get_param(params, vertex_root_t())); 233 } 234 235 template <class Graph, class ComponentMap> 236 inline typename property_traits<ComponentMap>::value_type strong_components(const Graph & g,ComponentMap comp BOOST_GRAPH_ENABLE_IF_MODELS_PARM (Graph,vertex_list_graph_tag))237 strong_components(const Graph& g, ComponentMap comp 238 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag)) 239 { 240 typedef typename graph_traits<Graph>::directed_category DirCat; 241 BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true)); 242 bgl_named_params<int, int> params(0); 243 return strong_components(g, comp, params); 244 } 245 246 template <typename Graph, typename ComponentMap, typename ComponentLists> build_component_lists(const Graph & g,typename graph_traits<Graph>::vertices_size_type num_scc,ComponentMap component_number,ComponentLists & components)247 void build_component_lists 248 (const Graph& g, 249 typename graph_traits<Graph>::vertices_size_type num_scc, 250 ComponentMap component_number, 251 ComponentLists& components) 252 { 253 components.resize(num_scc); 254 typename graph_traits<Graph>::vertex_iterator vi, vi_end; 255 for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi) 256 components[component_number[*vi]].push_back(*vi); 257 } 258 259 260 } // namespace boost 261 262 #include <queue> 263 #include <vector> 264 #include <boost/graph/transpose_graph.hpp> 265 #include <boost/pending/indirect_cmp.hpp> 266 #include <boost/graph/connected_components.hpp> // for components_recorder 267 268 namespace boost { 269 270 //========================================================================== 271 // This is the version of strongly connected components from 272 // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was 273 // adapted from "Data Structure and Algorithms" by Aho, Hopcroft, 274 // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir. 275 // The algorithm is based on computing DFS forests the graph 276 // and its transpose. 277 278 // This algorithm is slower than Tarjan's by a constant factor, uses 279 // more memory, and puts more requirements on the graph type. 280 281 template <class Graph, class DFSVisitor, class ComponentsMap, 282 class DiscoverTime, class FinishTime, 283 class ColorMap> 284 typename property_traits<ComponentsMap>::value_type kosaraju_strong_components(Graph & G,ComponentsMap c,FinishTime finish_time,ColorMap color)285 kosaraju_strong_components(Graph& G, ComponentsMap c, 286 FinishTime finish_time, ColorMap color) 287 { 288 BOOST_CONCEPT_ASSERT(( MutableGraphConcept<Graph> )); 289 // ... 290 291 typedef typename graph_traits<Graph>::vertex_descriptor Vertex; 292 typedef typename property_traits<ColorMap>::value_type ColorValue; 293 typedef color_traits<ColorValue> Color; 294 typename property_traits<FinishTime>::value_type time = 0; 295 depth_first_search 296 (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())), 297 color); 298 299 Graph G_T(num_vertices(G)); 300 transpose_graph(G, G_T); 301 302 typedef typename property_traits<ComponentsMap>::value_type count_type; 303 304 count_type c_count(0); 305 detail::components_recorder<ComponentsMap> 306 vis(c, c_count); 307 308 // initialize G_T 309 typename graph_traits<Graph>::vertex_iterator ui, ui_end; 310 for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui) 311 put(color, *ui, Color::white()); 312 313 typedef typename property_traits<FinishTime>::value_type D; 314 typedef indirect_cmp< FinishTime, std::less<D> > Compare; 315 316 Compare fl(finish_time); 317 std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl); 318 319 typename graph_traits<Graph>::vertex_iterator i, j, iend, jend; 320 boost::tie(i, iend) = vertices(G_T); 321 boost::tie(j, jend) = vertices(G); 322 for ( ; i != iend; ++i, ++j) { 323 put(finish_time, *i, get(finish_time, *j)); 324 Q.push(*i); 325 } 326 327 while ( !Q.empty() ) { 328 Vertex u = Q.top(); 329 Q.pop(); 330 if (get(color, u) == Color::white()) { 331 depth_first_visit(G_T, u, vis, color); 332 ++c_count; 333 } 334 } 335 return c_count; 336 } 337 338 } // namespace boost 339 340 #include BOOST_GRAPH_MPI_INCLUDE(<boost/graph/distributed/strong_components.hpp>) 341 342 #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP 343