[1077] | 1 | /* -*- C++ -*- |
---|
| 2 | * src/lemon/max_matching.h - Part of LEMON, a generic C++ optimization library |
---|
| 3 | * |
---|
[1164] | 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
[1077] | 6 | * |
---|
| 7 | * Permission to use, modify and distribute this software is granted |
---|
| 8 | * provided that this copyright notice appears in all copies. For |
---|
| 9 | * precise terms see the accompanying LICENSE file. |
---|
| 10 | * |
---|
| 11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
| 12 | * express or implied, and with no claim as to its suitability for any |
---|
| 13 | * purpose. |
---|
| 14 | * |
---|
| 15 | */ |
---|
| 16 | |
---|
| 17 | #ifndef LEMON_MAX_MATCHING_H |
---|
| 18 | #define LEMON_MAX_MATCHING_H |
---|
| 19 | |
---|
| 20 | #include <queue> |
---|
[1093] | 21 | #include <lemon/invalid.h> |
---|
| 22 | #include <lemon/unionfind.h> |
---|
[1077] | 23 | #include <lemon/graph_utils.h> |
---|
| 24 | |
---|
| 25 | ///\ingroup galgs |
---|
| 26 | ///\file |
---|
| 27 | ///\brief Maximum matching algorithm. |
---|
| 28 | |
---|
| 29 | namespace lemon { |
---|
| 30 | |
---|
| 31 | /// \addtogroup galgs |
---|
| 32 | /// @{ |
---|
| 33 | |
---|
| 34 | ///Edmonds' alternating forest maximum matching algorithm. |
---|
| 35 | |
---|
| 36 | ///This class provides Edmonds' alternating forest matching |
---|
| 37 | ///algorithm. The starting matching (if any) can be passed to the |
---|
| 38 | ///algorithm using read-in functions \ref readNMapNode, \ref |
---|
| 39 | ///readNMapEdge or \ref readEMapBool depending on the container. The |
---|
| 40 | ///resulting maximum matching can be attained by write-out functions |
---|
| 41 | ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool |
---|
| 42 | ///depending on the preferred container. |
---|
| 43 | /// |
---|
| 44 | ///The dual side of a matching is a map of the nodes to |
---|
| 45 | ///MaxMatching::pos_enum, having values D, A and C showing the |
---|
| 46 | ///Gallai-Edmonds decomposition of the graph. The nodes in D induce |
---|
| 47 | ///a graph with factor-critical components, the nodes in A form the |
---|
| 48 | ///barrier, and the nodes in C induce a graph having a perfect |
---|
| 49 | ///matching. This decomposition can be attained by calling \ref |
---|
[1090] | 50 | ///writePos after running the algorithm. |
---|
[1077] | 51 | /// |
---|
| 52 | ///\param Graph The undirected graph type the algorithm runs on. |
---|
| 53 | /// |
---|
| 54 | ///\author Jacint Szabo |
---|
| 55 | template <typename Graph> |
---|
| 56 | class MaxMatching { |
---|
[1165] | 57 | |
---|
| 58 | protected: |
---|
| 59 | |
---|
[1077] | 60 | typedef typename Graph::Node Node; |
---|
| 61 | typedef typename Graph::Edge Edge; |
---|
[1177] | 62 | typedef typename Graph::UndirEdge UndirEdge; |
---|
[1077] | 63 | typedef typename Graph::UndirEdgeIt UndirEdgeIt; |
---|
| 64 | typedef typename Graph::NodeIt NodeIt; |
---|
| 65 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
---|
| 66 | |
---|
| 67 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
---|
| 68 | |
---|
| 69 | public: |
---|
| 70 | |
---|
| 71 | ///Indicates the Gallai-Edmonds decomposition of the graph. |
---|
| 72 | |
---|
| 73 | ///Indicates the Gallai-Edmonds decomposition of the graph, which |
---|
| 74 | ///shows an upper bound on the size of a maximum matching. The |
---|
| 75 | ///nodes with pos_enum \c D induce a graph with factor-critical |
---|
| 76 | ///components, the nodes in \c A form the canonical barrier, and the |
---|
| 77 | ///nodes in \c C induce a graph having a perfect matching. |
---|
| 78 | enum pos_enum { |
---|
| 79 | D=0, |
---|
| 80 | A=1, |
---|
| 81 | C=2 |
---|
| 82 | }; |
---|
| 83 | |
---|
[1165] | 84 | protected: |
---|
[1077] | 85 | |
---|
| 86 | static const int HEUR_density=2; |
---|
| 87 | const Graph& g; |
---|
[1093] | 88 | typename Graph::template NodeMap<Node> _mate; |
---|
[1077] | 89 | typename Graph::template NodeMap<pos_enum> position; |
---|
| 90 | |
---|
| 91 | public: |
---|
| 92 | |
---|
[1093] | 93 | MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {} |
---|
[1077] | 94 | |
---|
| 95 | ///Runs Edmonds' algorithm. |
---|
| 96 | |
---|
| 97 | ///Runs Edmonds' algorithm for sparse graphs (number of edges < |
---|
| 98 | ///2*number of nodes), and a heuristical Edmonds' algorithm with a |
---|
[1090] | 99 | ///heuristic of postponing shrinks for dense graphs. |
---|
[1077] | 100 | inline void run(); |
---|
| 101 | |
---|
| 102 | ///Runs Edmonds' algorithm. |
---|
| 103 | |
---|
| 104 | ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs |
---|
| 105 | ///Edmonds' algorithm with a heuristic of postponing shrinks, |
---|
[1090] | 106 | ///giving a faster algorithm for dense graphs. |
---|
[1077] | 107 | void runEdmonds( int heur ); |
---|
| 108 | |
---|
| 109 | ///Finds a greedy matching starting from the actual matching. |
---|
| 110 | |
---|
| 111 | ///Starting form the actual matching stored, it finds a maximal |
---|
| 112 | ///greedy matching. |
---|
| 113 | void greedyMatching(); |
---|
| 114 | |
---|
| 115 | ///Returns the size of the actual matching stored. |
---|
| 116 | |
---|
| 117 | ///Returns the size of the actual matching stored. After \ref |
---|
| 118 | ///run() it returns the size of a maximum matching in the graph. |
---|
| 119 | int size() const; |
---|
| 120 | |
---|
| 121 | ///Resets the actual matching to the empty matching. |
---|
| 122 | |
---|
| 123 | ///Resets the actual matching to the empty matching. |
---|
| 124 | /// |
---|
| 125 | void resetMatching(); |
---|
| 126 | |
---|
[1093] | 127 | ///Returns the mate of a node in the actual matching. |
---|
| 128 | |
---|
| 129 | ///Returns the mate of a \c node in the actual matching. |
---|
| 130 | ///Returns INVALID if the \c node is not covered by the actual matching. |
---|
| 131 | Node mate(Node& node) const { |
---|
| 132 | return _mate[node]; |
---|
| 133 | } |
---|
| 134 | |
---|
[1165] | 135 | ///Reads a matching from a \c Node valued \c Node map. |
---|
[1077] | 136 | |
---|
[1165] | 137 | ///Reads a matching from a \c Node valued \c Node map. This map |
---|
| 138 | ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u |
---|
| 139 | ///must hold, and \c uv will be an edge of the matching. |
---|
[1077] | 140 | template<typename NMapN> |
---|
| 141 | void readNMapNode(NMapN& map) { |
---|
| 142 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 143 | _mate.set(v,map[v]); |
---|
[1077] | 144 | } |
---|
| 145 | } |
---|
| 146 | |
---|
[1165] | 147 | ///Writes the stored matching to a \c Node valued \c Node map. |
---|
[1077] | 148 | |
---|
[1165] | 149 | ///Writes the stored matching to a \c Node valued \c Node map. The |
---|
[1077] | 150 | ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c |
---|
| 151 | ///map[v]==u will hold, and now \c uv is an edge of the matching. |
---|
| 152 | template<typename NMapN> |
---|
| 153 | void writeNMapNode (NMapN& map) const { |
---|
| 154 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 155 | map.set(v,_mate[v]); |
---|
[1077] | 156 | } |
---|
| 157 | } |
---|
| 158 | |
---|
[1165] | 159 | ///Reads a matching from an \c UndirEdge valued \c Node map. |
---|
[1077] | 160 | |
---|
[1165] | 161 | ///Reads a matching from an \c UndirEdge valued \c Node map. \c |
---|
| 162 | ///map[v] must be an \c UndirEdge incident to \c v. This map must |
---|
| 163 | ///have the property that if \c g.oppositeNode(u,map[u])==v then |
---|
| 164 | ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge |
---|
[1172] | 165 | ///joining \c u to \c v will be an edge of the matching. |
---|
[1077] | 166 | template<typename NMapE> |
---|
| 167 | void readNMapEdge(NMapE& map) { |
---|
| 168 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1177] | 169 | UndirEdge e=map[v]; |
---|
[1165] | 170 | if ( e!=INVALID ) |
---|
[1166] | 171 | _mate.set(v,g.oppositeNode(v,e)); |
---|
[1077] | 172 | } |
---|
| 173 | } |
---|
| 174 | |
---|
[1165] | 175 | ///Writes the matching stored to an \c UndirEdge valued \c Node map. |
---|
[1077] | 176 | |
---|
[1165] | 177 | ///Writes the stored matching to an \c UndirEdge valued \c Node |
---|
| 178 | ///map. \c map[v] will be an \c UndirEdge incident to \c v. This |
---|
| 179 | ///map will have the property that if \c g.oppositeNode(u,map[u]) |
---|
| 180 | ///== v then \c map[u]==map[v] holds, and now this edge is an edge |
---|
| 181 | ///of the matching. |
---|
[1077] | 182 | template<typename NMapE> |
---|
| 183 | void writeNMapEdge (NMapE& map) const { |
---|
| 184 | typename Graph::template NodeMap<bool> todo(g,true); |
---|
| 185 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 186 | if ( todo[v] && _mate[v]!=INVALID ) { |
---|
| 187 | Node u=_mate[v]; |
---|
[1077] | 188 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
---|
[1158] | 189 | if ( g.runningNode(e) == u ) { |
---|
[1077] | 190 | map.set(u,e); |
---|
| 191 | map.set(v,e); |
---|
| 192 | todo.set(u,false); |
---|
| 193 | todo.set(v,false); |
---|
| 194 | break; |
---|
| 195 | } |
---|
| 196 | } |
---|
| 197 | } |
---|
| 198 | } |
---|
| 199 | } |
---|
| 200 | |
---|
| 201 | |
---|
[1165] | 202 | ///Reads a matching from a \c bool valued \c Edge map. |
---|
[1077] | 203 | |
---|
[1165] | 204 | ///Reads a matching from a \c bool valued \c Edge map. This map |
---|
| 205 | ///must have the property that there are no two incident edges \c |
---|
| 206 | ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c |
---|
[1077] | 207 | ///map[e]==true form the matching. |
---|
| 208 | template<typename EMapB> |
---|
| 209 | void readEMapBool(EMapB& map) { |
---|
| 210 | for(UndirEdgeIt e(g); e!=INVALID; ++e) { |
---|
| 211 | if ( map[e] ) { |
---|
| 212 | Node u=g.source(e); |
---|
| 213 | Node v=g.target(e); |
---|
[1093] | 214 | _mate.set(u,v); |
---|
| 215 | _mate.set(v,u); |
---|
[1077] | 216 | } |
---|
| 217 | } |
---|
| 218 | } |
---|
| 219 | |
---|
| 220 | |
---|
[1165] | 221 | ///Writes the matching stored to a \c bool valued \c Edge map. |
---|
[1077] | 222 | |
---|
[1165] | 223 | ///Writes the matching stored to a \c bool valued \c Edge |
---|
| 224 | ///map. This map will have the property that there are no two |
---|
| 225 | ///incident edges \c e, \c f with \c map[e]==map[f]==true. The |
---|
| 226 | ///edges \c e with \c map[e]==true form the matching. |
---|
[1077] | 227 | template<typename EMapB> |
---|
| 228 | void writeEMapBool (EMapB& map) const { |
---|
| 229 | for(UndirEdgeIt e(g); e!=INVALID; ++e) map.set(e,false); |
---|
| 230 | |
---|
| 231 | typename Graph::template NodeMap<bool> todo(g,true); |
---|
| 232 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 233 | if ( todo[v] && _mate[v]!=INVALID ) { |
---|
| 234 | Node u=_mate[v]; |
---|
[1077] | 235 | for(IncEdgeIt e(g,v); e!=INVALID; ++e) { |
---|
[1158] | 236 | if ( g.runningNode(e) == u ) { |
---|
[1077] | 237 | map.set(e,true); |
---|
| 238 | todo.set(u,false); |
---|
| 239 | todo.set(v,false); |
---|
| 240 | break; |
---|
| 241 | } |
---|
| 242 | } |
---|
| 243 | } |
---|
| 244 | } |
---|
| 245 | } |
---|
| 246 | |
---|
| 247 | |
---|
| 248 | ///Writes the canonical decomposition of the graph after running |
---|
| 249 | ///the algorithm. |
---|
| 250 | |
---|
[1090] | 251 | ///After calling any run methods of the class, it writes the |
---|
| 252 | ///Gallai-Edmonds canonical decomposition of the graph. \c map |
---|
| 253 | ///must be a node map of \ref pos_enum 's. |
---|
[1077] | 254 | template<typename NMapEnum> |
---|
| 255 | void writePos (NMapEnum& map) const { |
---|
| 256 | for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]); |
---|
| 257 | } |
---|
| 258 | |
---|
| 259 | private: |
---|
| 260 | |
---|
[1165] | 261 | |
---|
[1077] | 262 | void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
| 263 | UFE& blossom, UFE& tree); |
---|
| 264 | |
---|
[1234] | 265 | void normShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
[1077] | 266 | UFE& blossom, UFE& tree); |
---|
| 267 | |
---|
[1234] | 268 | bool noShrinkStep(Node x, typename Graph::template NodeMap<Node>& ear, |
---|
[1077] | 269 | UFE& blossom, UFE& tree, std::queue<Node>& Q); |
---|
| 270 | |
---|
[1234] | 271 | void shrinkStep(Node& top, Node& middle, Node& bottom, |
---|
| 272 | typename Graph::template NodeMap<Node>& ear, |
---|
[1077] | 273 | UFE& blossom, UFE& tree, std::queue<Node>& Q); |
---|
| 274 | |
---|
[1234] | 275 | void augment(Node x, typename Graph::template NodeMap<Node>& ear, |
---|
[1077] | 276 | UFE& blossom, UFE& tree); |
---|
| 277 | |
---|
| 278 | }; |
---|
| 279 | |
---|
| 280 | |
---|
| 281 | // ********************************************************************** |
---|
| 282 | // IMPLEMENTATIONS |
---|
| 283 | // ********************************************************************** |
---|
| 284 | |
---|
| 285 | |
---|
| 286 | template <typename Graph> |
---|
| 287 | void MaxMatching<Graph>::run() { |
---|
| 288 | if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) { |
---|
| 289 | greedyMatching(); |
---|
| 290 | runEdmonds(0); |
---|
| 291 | } else runEdmonds(1); |
---|
| 292 | } |
---|
| 293 | |
---|
| 294 | |
---|
| 295 | template <typename Graph> |
---|
| 296 | void MaxMatching<Graph>::runEdmonds( int heur=1 ) { |
---|
[1090] | 297 | |
---|
| 298 | for(NodeIt v(g); v!=INVALID; ++v) |
---|
| 299 | position.set(v,C); |
---|
| 300 | |
---|
[1077] | 301 | typename Graph::template NodeMap<Node> ear(g,INVALID); |
---|
| 302 | //undefined for the base nodes of the blossoms (i.e. for the |
---|
[1165] | 303 | //representative elements of UFE blossom) and for the nodes in C |
---|
| 304 | |
---|
[1077] | 305 | typename UFE::MapType blossom_base(g); |
---|
| 306 | UFE blossom(blossom_base); |
---|
| 307 | typename UFE::MapType tree_base(g); |
---|
| 308 | UFE tree(tree_base); |
---|
[1165] | 309 | //If these UFE's would be members of the class then also |
---|
| 310 | //blossom_base and tree_base should be a member. |
---|
[1077] | 311 | |
---|
| 312 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 313 | if ( position[v]==C && _mate[v]==INVALID ) { |
---|
[1077] | 314 | blossom.insert(v); |
---|
| 315 | tree.insert(v); |
---|
| 316 | position.set(v,D); |
---|
| 317 | if ( heur == 1 ) lateShrink( v, ear, blossom, tree ); |
---|
| 318 | else normShrink( v, ear, blossom, tree ); |
---|
| 319 | } |
---|
| 320 | } |
---|
| 321 | } |
---|
| 322 | |
---|
| 323 | |
---|
| 324 | template <typename Graph> |
---|
| 325 | void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear, |
---|
| 326 | UFE& blossom, UFE& tree) { |
---|
| 327 | |
---|
| 328 | std::queue<Node> Q; //queue of the totally unscanned nodes |
---|
| 329 | Q.push(v); |
---|
| 330 | std::queue<Node> R; |
---|
| 331 | //queue of the nodes which must be scanned for a possible shrink |
---|
| 332 | |
---|
| 333 | while ( !Q.empty() ) { |
---|
| 334 | Node x=Q.front(); |
---|
| 335 | Q.pop(); |
---|
| 336 | if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return; |
---|
| 337 | else R.push(x); |
---|
| 338 | } |
---|
| 339 | |
---|
| 340 | while ( !R.empty() ) { |
---|
| 341 | Node x=R.front(); |
---|
| 342 | R.pop(); |
---|
| 343 | |
---|
| 344 | for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) { |
---|
[1158] | 345 | Node y=g.runningNode(e); |
---|
[1077] | 346 | |
---|
| 347 | if ( position[y] == D && blossom.find(x) != blossom.find(y) ) { |
---|
| 348 | //x and y must be in the same tree |
---|
| 349 | |
---|
| 350 | typename Graph::template NodeMap<bool> path(g,false); |
---|
| 351 | |
---|
| 352 | Node b=blossom.find(x); |
---|
| 353 | path.set(b,true); |
---|
[1093] | 354 | b=_mate[b]; |
---|
[1077] | 355 | while ( b!=INVALID ) { |
---|
| 356 | b=blossom.find(ear[b]); |
---|
| 357 | path.set(b,true); |
---|
[1093] | 358 | b=_mate[b]; |
---|
[1077] | 359 | } //going till the root |
---|
| 360 | |
---|
| 361 | Node top=y; |
---|
| 362 | Node middle=blossom.find(top); |
---|
| 363 | Node bottom=x; |
---|
| 364 | while ( !path[middle] ) |
---|
| 365 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
| 366 | |
---|
| 367 | Node base=middle; |
---|
| 368 | top=x; |
---|
| 369 | middle=blossom.find(top); |
---|
| 370 | bottom=y; |
---|
| 371 | Node blossom_base=blossom.find(base); |
---|
| 372 | while ( middle!=blossom_base ) |
---|
| 373 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
| 374 | |
---|
| 375 | blossom.makeRep(base); |
---|
| 376 | } // if shrink is needed |
---|
| 377 | |
---|
| 378 | while ( !Q.empty() ) { |
---|
| 379 | Node x=Q.front(); |
---|
| 380 | Q.pop(); |
---|
| 381 | if ( noShrinkStep(x, ear, blossom, tree, Q) ) return; |
---|
| 382 | else R.push(x); |
---|
| 383 | } |
---|
| 384 | } //for e |
---|
| 385 | } // while ( !R.empty() ) |
---|
| 386 | } |
---|
| 387 | |
---|
| 388 | |
---|
| 389 | template <typename Graph> |
---|
[1234] | 390 | void MaxMatching<Graph>::normShrink(Node v, |
---|
| 391 | typename Graph::template |
---|
| 392 | NodeMap<Node>& ear, |
---|
[1077] | 393 | UFE& blossom, UFE& tree) { |
---|
| 394 | std::queue<Node> Q; //queue of the unscanned nodes |
---|
| 395 | Q.push(v); |
---|
| 396 | while ( !Q.empty() ) { |
---|
| 397 | |
---|
| 398 | Node x=Q.front(); |
---|
| 399 | Q.pop(); |
---|
| 400 | |
---|
| 401 | for( IncEdgeIt e(g,x); e!=INVALID; ++e ) { |
---|
[1158] | 402 | Node y=g.runningNode(e); |
---|
[1077] | 403 | |
---|
| 404 | switch ( position[y] ) { |
---|
| 405 | case D: //x and y must be in the same tree |
---|
| 406 | |
---|
| 407 | if ( blossom.find(x) != blossom.find(y) ) { //shrink |
---|
| 408 | typename Graph::template NodeMap<bool> path(g,false); |
---|
| 409 | |
---|
| 410 | Node b=blossom.find(x); |
---|
| 411 | path.set(b,true); |
---|
[1093] | 412 | b=_mate[b]; |
---|
[1077] | 413 | while ( b!=INVALID ) { |
---|
| 414 | b=blossom.find(ear[b]); |
---|
| 415 | path.set(b,true); |
---|
[1093] | 416 | b=_mate[b]; |
---|
[1077] | 417 | } //going till the root |
---|
| 418 | |
---|
| 419 | Node top=y; |
---|
| 420 | Node middle=blossom.find(top); |
---|
| 421 | Node bottom=x; |
---|
| 422 | while ( !path[middle] ) |
---|
| 423 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
| 424 | |
---|
| 425 | Node base=middle; |
---|
| 426 | top=x; |
---|
| 427 | middle=blossom.find(top); |
---|
| 428 | bottom=y; |
---|
| 429 | Node blossom_base=blossom.find(base); |
---|
| 430 | while ( middle!=blossom_base ) |
---|
| 431 | shrinkStep(top, middle, bottom, ear, blossom, tree, Q); |
---|
| 432 | |
---|
| 433 | blossom.makeRep(base); |
---|
| 434 | } |
---|
| 435 | break; |
---|
| 436 | case C: |
---|
[1093] | 437 | if ( _mate[y]!=INVALID ) { //grow |
---|
[1077] | 438 | |
---|
| 439 | ear.set(y,x); |
---|
[1093] | 440 | Node w=_mate[y]; |
---|
[1077] | 441 | blossom.insert(w); |
---|
| 442 | position.set(y,A); |
---|
| 443 | position.set(w,D); |
---|
| 444 | tree.insert(y); |
---|
| 445 | tree.insert(w); |
---|
| 446 | tree.join(y,blossom.find(x)); |
---|
| 447 | tree.join(w,y); |
---|
| 448 | Q.push(w); |
---|
| 449 | } else { //augment |
---|
| 450 | augment(x, ear, blossom, tree); |
---|
[1093] | 451 | _mate.set(x,y); |
---|
| 452 | _mate.set(y,x); |
---|
[1077] | 453 | return; |
---|
| 454 | } //if |
---|
| 455 | break; |
---|
| 456 | default: break; |
---|
| 457 | } |
---|
| 458 | } |
---|
| 459 | } |
---|
| 460 | } |
---|
| 461 | |
---|
| 462 | template <typename Graph> |
---|
| 463 | void MaxMatching<Graph>::greedyMatching() { |
---|
| 464 | for(NodeIt v(g); v!=INVALID; ++v) |
---|
[1093] | 465 | if ( _mate[v]==INVALID ) { |
---|
[1077] | 466 | for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) { |
---|
[1158] | 467 | Node y=g.runningNode(e); |
---|
[1093] | 468 | if ( _mate[y]==INVALID && y!=v ) { |
---|
| 469 | _mate.set(v,y); |
---|
| 470 | _mate.set(y,v); |
---|
[1077] | 471 | break; |
---|
| 472 | } |
---|
| 473 | } |
---|
| 474 | } |
---|
| 475 | } |
---|
| 476 | |
---|
| 477 | template <typename Graph> |
---|
| 478 | int MaxMatching<Graph>::size() const { |
---|
| 479 | int s=0; |
---|
| 480 | for(NodeIt v(g); v!=INVALID; ++v) { |
---|
[1093] | 481 | if ( _mate[v]!=INVALID ) { |
---|
[1077] | 482 | ++s; |
---|
| 483 | } |
---|
| 484 | } |
---|
[1165] | 485 | return s/2; |
---|
[1077] | 486 | } |
---|
| 487 | |
---|
| 488 | template <typename Graph> |
---|
| 489 | void MaxMatching<Graph>::resetMatching() { |
---|
| 490 | for(NodeIt v(g); v!=INVALID; ++v) |
---|
[1093] | 491 | _mate.set(v,INVALID); |
---|
[1077] | 492 | } |
---|
| 493 | |
---|
| 494 | template <typename Graph> |
---|
[1234] | 495 | bool MaxMatching<Graph>::noShrinkStep(Node x, |
---|
| 496 | typename Graph::template |
---|
| 497 | NodeMap<Node>& ear, |
---|
| 498 | UFE& blossom, UFE& tree, |
---|
| 499 | std::queue<Node>& Q) { |
---|
[1077] | 500 | for( IncEdgeIt e(g,x); e!= INVALID; ++e ) { |
---|
[1158] | 501 | Node y=g.runningNode(e); |
---|
[1077] | 502 | |
---|
| 503 | if ( position[y]==C ) { |
---|
[1093] | 504 | if ( _mate[y]!=INVALID ) { //grow |
---|
[1077] | 505 | ear.set(y,x); |
---|
[1093] | 506 | Node w=_mate[y]; |
---|
[1077] | 507 | blossom.insert(w); |
---|
| 508 | position.set(y,A); |
---|
| 509 | position.set(w,D); |
---|
| 510 | tree.insert(y); |
---|
| 511 | tree.insert(w); |
---|
| 512 | tree.join(y,blossom.find(x)); |
---|
| 513 | tree.join(w,y); |
---|
| 514 | Q.push(w); |
---|
| 515 | } else { //augment |
---|
| 516 | augment(x, ear, blossom, tree); |
---|
[1093] | 517 | _mate.set(x,y); |
---|
| 518 | _mate.set(y,x); |
---|
[1077] | 519 | return true; |
---|
| 520 | } |
---|
| 521 | } |
---|
| 522 | } |
---|
| 523 | return false; |
---|
| 524 | } |
---|
| 525 | |
---|
| 526 | template <typename Graph> |
---|
[1234] | 527 | void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, |
---|
| 528 | typename Graph::template |
---|
| 529 | NodeMap<Node>& ear, |
---|
| 530 | UFE& blossom, UFE& tree, |
---|
| 531 | std::queue<Node>& Q) { |
---|
[1077] | 532 | ear.set(top,bottom); |
---|
| 533 | Node t=top; |
---|
| 534 | while ( t!=middle ) { |
---|
[1093] | 535 | Node u=_mate[t]; |
---|
[1077] | 536 | t=ear[u]; |
---|
| 537 | ear.set(t,u); |
---|
| 538 | } |
---|
[1093] | 539 | bottom=_mate[middle]; |
---|
[1077] | 540 | position.set(bottom,D); |
---|
| 541 | Q.push(bottom); |
---|
| 542 | top=ear[bottom]; |
---|
| 543 | Node oldmiddle=middle; |
---|
| 544 | middle=blossom.find(top); |
---|
| 545 | tree.erase(bottom); |
---|
| 546 | tree.erase(oldmiddle); |
---|
| 547 | blossom.insert(bottom); |
---|
| 548 | blossom.join(bottom, oldmiddle); |
---|
| 549 | blossom.join(top, oldmiddle); |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | template <typename Graph> |
---|
[1234] | 553 | void MaxMatching<Graph>::augment(Node x, |
---|
| 554 | typename Graph::template NodeMap<Node>& ear, |
---|
[1077] | 555 | UFE& blossom, UFE& tree) { |
---|
[1093] | 556 | Node v=_mate[x]; |
---|
[1077] | 557 | while ( v!=INVALID ) { |
---|
| 558 | |
---|
| 559 | Node u=ear[v]; |
---|
[1093] | 560 | _mate.set(v,u); |
---|
[1077] | 561 | Node tmp=v; |
---|
[1093] | 562 | v=_mate[u]; |
---|
| 563 | _mate.set(u,tmp); |
---|
[1077] | 564 | } |
---|
| 565 | typename UFE::ItemIt it; |
---|
| 566 | for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) { |
---|
| 567 | if ( position[it] == D ) { |
---|
| 568 | typename UFE::ItemIt b_it; |
---|
| 569 | for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) { |
---|
| 570 | position.set( b_it ,C); |
---|
| 571 | } |
---|
| 572 | blossom.eraseClass(it); |
---|
| 573 | } else position.set( it ,C); |
---|
| 574 | } |
---|
| 575 | tree.eraseClass(x); |
---|
| 576 | |
---|
| 577 | } |
---|
| 578 | |
---|
| 579 | /// @} |
---|
| 580 | |
---|
| 581 | } //END OF NAMESPACE LEMON |
---|
| 582 | |
---|
[1165] | 583 | #endif //LEMON_MAX_MATCHING_H |
---|