1.1 --- a/src/lemon/max_matching.h Sat May 21 21:04:57 2005 +0000
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,583 +0,0 @@
1.4 -/* -*- C++ -*-
1.5 - * src/lemon/max_matching.h - Part of LEMON, a generic C++ optimization library
1.6 - *
1.7 - * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 - * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.9 - *
1.10 - * Permission to use, modify and distribute this software is granted
1.11 - * provided that this copyright notice appears in all copies. For
1.12 - * precise terms see the accompanying LICENSE file.
1.13 - *
1.14 - * This software is provided "AS IS" with no warranty of any kind,
1.15 - * express or implied, and with no claim as to its suitability for any
1.16 - * purpose.
1.17 - *
1.18 - */
1.19 -
1.20 -#ifndef LEMON_MAX_MATCHING_H
1.21 -#define LEMON_MAX_MATCHING_H
1.22 -
1.23 -#include <queue>
1.24 -#include <lemon/invalid.h>
1.25 -#include <lemon/unionfind.h>
1.26 -#include <lemon/graph_utils.h>
1.27 -
1.28 -///\ingroup galgs
1.29 -///\file
1.30 -///\brief Maximum matching algorithm.
1.31 -
1.32 -namespace lemon {
1.33 -
1.34 - /// \addtogroup galgs
1.35 - /// @{
1.36 -
1.37 - ///Edmonds' alternating forest maximum matching algorithm.
1.38 -
1.39 - ///This class provides Edmonds' alternating forest matching
1.40 - ///algorithm. The starting matching (if any) can be passed to the
1.41 - ///algorithm using read-in functions \ref readNMapNode, \ref
1.42 - ///readNMapEdge or \ref readEMapBool depending on the container. The
1.43 - ///resulting maximum matching can be attained by write-out functions
1.44 - ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
1.45 - ///depending on the preferred container.
1.46 - ///
1.47 - ///The dual side of a matching is a map of the nodes to
1.48 - ///MaxMatching::pos_enum, having values D, A and C showing the
1.49 - ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
1.50 - ///a graph with factor-critical components, the nodes in A form the
1.51 - ///barrier, and the nodes in C induce a graph having a perfect
1.52 - ///matching. This decomposition can be attained by calling \ref
1.53 - ///writePos after running the algorithm.
1.54 - ///
1.55 - ///\param Graph The undirected graph type the algorithm runs on.
1.56 - ///
1.57 - ///\author Jacint Szabo
1.58 - template <typename Graph>
1.59 - class MaxMatching {
1.60 -
1.61 - protected:
1.62 -
1.63 - typedef typename Graph::Node Node;
1.64 - typedef typename Graph::Edge Edge;
1.65 - typedef typename Graph::UndirEdge UndirEdge;
1.66 - typedef typename Graph::UndirEdgeIt UndirEdgeIt;
1.67 - typedef typename Graph::NodeIt NodeIt;
1.68 - typedef typename Graph::IncEdgeIt IncEdgeIt;
1.69 -
1.70 - typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
1.71 -
1.72 - public:
1.73 -
1.74 - ///Indicates the Gallai-Edmonds decomposition of the graph.
1.75 -
1.76 - ///Indicates the Gallai-Edmonds decomposition of the graph, which
1.77 - ///shows an upper bound on the size of a maximum matching. The
1.78 - ///nodes with pos_enum \c D induce a graph with factor-critical
1.79 - ///components, the nodes in \c A form the canonical barrier, and the
1.80 - ///nodes in \c C induce a graph having a perfect matching.
1.81 - enum pos_enum {
1.82 - D=0,
1.83 - A=1,
1.84 - C=2
1.85 - };
1.86 -
1.87 - protected:
1.88 -
1.89 - static const int HEUR_density=2;
1.90 - const Graph& g;
1.91 - typename Graph::template NodeMap<Node> _mate;
1.92 - typename Graph::template NodeMap<pos_enum> position;
1.93 -
1.94 - public:
1.95 -
1.96 - MaxMatching(const Graph& _g) : g(_g), _mate(_g,INVALID), position(_g) {}
1.97 -
1.98 - ///Runs Edmonds' algorithm.
1.99 -
1.100 - ///Runs Edmonds' algorithm for sparse graphs (number of edges <
1.101 - ///2*number of nodes), and a heuristical Edmonds' algorithm with a
1.102 - ///heuristic of postponing shrinks for dense graphs.
1.103 - inline void run();
1.104 -
1.105 - ///Runs Edmonds' algorithm.
1.106 -
1.107 - ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
1.108 - ///Edmonds' algorithm with a heuristic of postponing shrinks,
1.109 - ///giving a faster algorithm for dense graphs.
1.110 - void runEdmonds( int heur );
1.111 -
1.112 - ///Finds a greedy matching starting from the actual matching.
1.113 -
1.114 - ///Starting form the actual matching stored, it finds a maximal
1.115 - ///greedy matching.
1.116 - void greedyMatching();
1.117 -
1.118 - ///Returns the size of the actual matching stored.
1.119 -
1.120 - ///Returns the size of the actual matching stored. After \ref
1.121 - ///run() it returns the size of a maximum matching in the graph.
1.122 - int size() const;
1.123 -
1.124 - ///Resets the actual matching to the empty matching.
1.125 -
1.126 - ///Resets the actual matching to the empty matching.
1.127 - ///
1.128 - void resetMatching();
1.129 -
1.130 - ///Returns the mate of a node in the actual matching.
1.131 -
1.132 - ///Returns the mate of a \c node in the actual matching.
1.133 - ///Returns INVALID if the \c node is not covered by the actual matching.
1.134 - Node mate(Node& node) const {
1.135 - return _mate[node];
1.136 - }
1.137 -
1.138 - ///Reads a matching from a \c Node valued \c Node map.
1.139 -
1.140 - ///Reads a matching from a \c Node valued \c Node map. This map
1.141 - ///must be \e symmetric, i.e. if \c map[u]==v then \c map[v]==u
1.142 - ///must hold, and \c uv will be an edge of the matching.
1.143 - template<typename NMapN>
1.144 - void readNMapNode(NMapN& map) {
1.145 - for(NodeIt v(g); v!=INVALID; ++v) {
1.146 - _mate.set(v,map[v]);
1.147 - }
1.148 - }
1.149 -
1.150 - ///Writes the stored matching to a \c Node valued \c Node map.
1.151 -
1.152 - ///Writes the stored matching to a \c Node valued \c Node map. The
1.153 - ///resulting map will be \e symmetric, i.e. if \c map[u]==v then \c
1.154 - ///map[v]==u will hold, and now \c uv is an edge of the matching.
1.155 - template<typename NMapN>
1.156 - void writeNMapNode (NMapN& map) const {
1.157 - for(NodeIt v(g); v!=INVALID; ++v) {
1.158 - map.set(v,_mate[v]);
1.159 - }
1.160 - }
1.161 -
1.162 - ///Reads a matching from an \c UndirEdge valued \c Node map.
1.163 -
1.164 - ///Reads a matching from an \c UndirEdge valued \c Node map. \c
1.165 - ///map[v] must be an \c UndirEdge incident to \c v. This map must
1.166 - ///have the property that if \c g.oppositeNode(u,map[u])==v then
1.167 - ///\c \c g.oppositeNode(v,map[v])==u holds, and now some edge
1.168 - ///joining \c u to \c v will be an edge of the matching.
1.169 - template<typename NMapE>
1.170 - void readNMapEdge(NMapE& map) {
1.171 - for(NodeIt v(g); v!=INVALID; ++v) {
1.172 - UndirEdge e=map[v];
1.173 - if ( e!=INVALID )
1.174 - _mate.set(v,g.oppositeNode(v,e));
1.175 - }
1.176 - }
1.177 -
1.178 - ///Writes the matching stored to an \c UndirEdge valued \c Node map.
1.179 -
1.180 - ///Writes the stored matching to an \c UndirEdge valued \c Node
1.181 - ///map. \c map[v] will be an \c UndirEdge incident to \c v. This
1.182 - ///map will have the property that if \c g.oppositeNode(u,map[u])
1.183 - ///== v then \c map[u]==map[v] holds, and now this edge is an edge
1.184 - ///of the matching.
1.185 - template<typename NMapE>
1.186 - void writeNMapEdge (NMapE& map) const {
1.187 - typename Graph::template NodeMap<bool> todo(g,true);
1.188 - for(NodeIt v(g); v!=INVALID; ++v) {
1.189 - if ( todo[v] && _mate[v]!=INVALID ) {
1.190 - Node u=_mate[v];
1.191 - for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
1.192 - if ( g.runningNode(e) == u ) {
1.193 - map.set(u,e);
1.194 - map.set(v,e);
1.195 - todo.set(u,false);
1.196 - todo.set(v,false);
1.197 - break;
1.198 - }
1.199 - }
1.200 - }
1.201 - }
1.202 - }
1.203 -
1.204 -
1.205 - ///Reads a matching from a \c bool valued \c Edge map.
1.206 -
1.207 - ///Reads a matching from a \c bool valued \c Edge map. This map
1.208 - ///must have the property that there are no two incident edges \c
1.209 - ///e, \c f with \c map[e]==map[f]==true. The edges \c e with \c
1.210 - ///map[e]==true form the matching.
1.211 - template<typename EMapB>
1.212 - void readEMapBool(EMapB& map) {
1.213 - for(UndirEdgeIt e(g); e!=INVALID; ++e) {
1.214 - if ( map[e] ) {
1.215 - Node u=g.source(e);
1.216 - Node v=g.target(e);
1.217 - _mate.set(u,v);
1.218 - _mate.set(v,u);
1.219 - }
1.220 - }
1.221 - }
1.222 -
1.223 -
1.224 - ///Writes the matching stored to a \c bool valued \c Edge map.
1.225 -
1.226 - ///Writes the matching stored to a \c bool valued \c Edge
1.227 - ///map. This map will have the property that there are no two
1.228 - ///incident edges \c e, \c f with \c map[e]==map[f]==true. The
1.229 - ///edges \c e with \c map[e]==true form the matching.
1.230 - template<typename EMapB>
1.231 - void writeEMapBool (EMapB& map) const {
1.232 - for(UndirEdgeIt e(g); e!=INVALID; ++e) map.set(e,false);
1.233 -
1.234 - typename Graph::template NodeMap<bool> todo(g,true);
1.235 - for(NodeIt v(g); v!=INVALID; ++v) {
1.236 - if ( todo[v] && _mate[v]!=INVALID ) {
1.237 - Node u=_mate[v];
1.238 - for(IncEdgeIt e(g,v); e!=INVALID; ++e) {
1.239 - if ( g.runningNode(e) == u ) {
1.240 - map.set(e,true);
1.241 - todo.set(u,false);
1.242 - todo.set(v,false);
1.243 - break;
1.244 - }
1.245 - }
1.246 - }
1.247 - }
1.248 - }
1.249 -
1.250 -
1.251 - ///Writes the canonical decomposition of the graph after running
1.252 - ///the algorithm.
1.253 -
1.254 - ///After calling any run methods of the class, it writes the
1.255 - ///Gallai-Edmonds canonical decomposition of the graph. \c map
1.256 - ///must be a node map of \ref pos_enum 's.
1.257 - template<typename NMapEnum>
1.258 - void writePos (NMapEnum& map) const {
1.259 - for(NodeIt v(g); v!=INVALID; ++v) map.set(v,position[v]);
1.260 - }
1.261 -
1.262 - private:
1.263 -
1.264 -
1.265 - void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.266 - UFE& blossom, UFE& tree);
1.267 -
1.268 - void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.269 - UFE& blossom, UFE& tree);
1.270 -
1.271 - bool noShrinkStep(Node x, typename Graph::template NodeMap<Node>& ear,
1.272 - UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.273 -
1.274 - void shrinkStep(Node& top, Node& middle, Node& bottom,
1.275 - typename Graph::template NodeMap<Node>& ear,
1.276 - UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.277 -
1.278 - void augment(Node x, typename Graph::template NodeMap<Node>& ear,
1.279 - UFE& blossom, UFE& tree);
1.280 -
1.281 - };
1.282 -
1.283 -
1.284 - // **********************************************************************
1.285 - // IMPLEMENTATIONS
1.286 - // **********************************************************************
1.287 -
1.288 -
1.289 - template <typename Graph>
1.290 - void MaxMatching<Graph>::run() {
1.291 - if ( countUndirEdges(g) < HEUR_density*countNodes(g) ) {
1.292 - greedyMatching();
1.293 - runEdmonds(0);
1.294 - } else runEdmonds(1);
1.295 - }
1.296 -
1.297 -
1.298 - template <typename Graph>
1.299 - void MaxMatching<Graph>::runEdmonds( int heur=1 ) {
1.300 -
1.301 - for(NodeIt v(g); v!=INVALID; ++v)
1.302 - position.set(v,C);
1.303 -
1.304 - typename Graph::template NodeMap<Node> ear(g,INVALID);
1.305 - //undefined for the base nodes of the blossoms (i.e. for the
1.306 - //representative elements of UFE blossom) and for the nodes in C
1.307 -
1.308 - typename UFE::MapType blossom_base(g);
1.309 - UFE blossom(blossom_base);
1.310 - typename UFE::MapType tree_base(g);
1.311 - UFE tree(tree_base);
1.312 - //If these UFE's would be members of the class then also
1.313 - //blossom_base and tree_base should be a member.
1.314 -
1.315 - for(NodeIt v(g); v!=INVALID; ++v) {
1.316 - if ( position[v]==C && _mate[v]==INVALID ) {
1.317 - blossom.insert(v);
1.318 - tree.insert(v);
1.319 - position.set(v,D);
1.320 - if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
1.321 - else normShrink( v, ear, blossom, tree );
1.322 - }
1.323 - }
1.324 - }
1.325 -
1.326 -
1.327 - template <typename Graph>
1.328 - void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.329 - UFE& blossom, UFE& tree) {
1.330 -
1.331 - std::queue<Node> Q; //queue of the totally unscanned nodes
1.332 - Q.push(v);
1.333 - std::queue<Node> R;
1.334 - //queue of the nodes which must be scanned for a possible shrink
1.335 -
1.336 - while ( !Q.empty() ) {
1.337 - Node x=Q.front();
1.338 - Q.pop();
1.339 - if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
1.340 - else R.push(x);
1.341 - }
1.342 -
1.343 - while ( !R.empty() ) {
1.344 - Node x=R.front();
1.345 - R.pop();
1.346 -
1.347 - for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
1.348 - Node y=g.runningNode(e);
1.349 -
1.350 - if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
1.351 - //x and y must be in the same tree
1.352 -
1.353 - typename Graph::template NodeMap<bool> path(g,false);
1.354 -
1.355 - Node b=blossom.find(x);
1.356 - path.set(b,true);
1.357 - b=_mate[b];
1.358 - while ( b!=INVALID ) {
1.359 - b=blossom.find(ear[b]);
1.360 - path.set(b,true);
1.361 - b=_mate[b];
1.362 - } //going till the root
1.363 -
1.364 - Node top=y;
1.365 - Node middle=blossom.find(top);
1.366 - Node bottom=x;
1.367 - while ( !path[middle] )
1.368 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.369 -
1.370 - Node base=middle;
1.371 - top=x;
1.372 - middle=blossom.find(top);
1.373 - bottom=y;
1.374 - Node blossom_base=blossom.find(base);
1.375 - while ( middle!=blossom_base )
1.376 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.377 -
1.378 - blossom.makeRep(base);
1.379 - } // if shrink is needed
1.380 -
1.381 - while ( !Q.empty() ) {
1.382 - Node x=Q.front();
1.383 - Q.pop();
1.384 - if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
1.385 - else R.push(x);
1.386 - }
1.387 - } //for e
1.388 - } // while ( !R.empty() )
1.389 - }
1.390 -
1.391 -
1.392 - template <typename Graph>
1.393 - void MaxMatching<Graph>::normShrink(Node v,
1.394 - typename Graph::template
1.395 - NodeMap<Node>& ear,
1.396 - UFE& blossom, UFE& tree) {
1.397 - std::queue<Node> Q; //queue of the unscanned nodes
1.398 - Q.push(v);
1.399 - while ( !Q.empty() ) {
1.400 -
1.401 - Node x=Q.front();
1.402 - Q.pop();
1.403 -
1.404 - for( IncEdgeIt e(g,x); e!=INVALID; ++e ) {
1.405 - Node y=g.runningNode(e);
1.406 -
1.407 - switch ( position[y] ) {
1.408 - case D: //x and y must be in the same tree
1.409 -
1.410 - if ( blossom.find(x) != blossom.find(y) ) { //shrink
1.411 - typename Graph::template NodeMap<bool> path(g,false);
1.412 -
1.413 - Node b=blossom.find(x);
1.414 - path.set(b,true);
1.415 - b=_mate[b];
1.416 - while ( b!=INVALID ) {
1.417 - b=blossom.find(ear[b]);
1.418 - path.set(b,true);
1.419 - b=_mate[b];
1.420 - } //going till the root
1.421 -
1.422 - Node top=y;
1.423 - Node middle=blossom.find(top);
1.424 - Node bottom=x;
1.425 - while ( !path[middle] )
1.426 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.427 -
1.428 - Node base=middle;
1.429 - top=x;
1.430 - middle=blossom.find(top);
1.431 - bottom=y;
1.432 - Node blossom_base=blossom.find(base);
1.433 - while ( middle!=blossom_base )
1.434 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.435 -
1.436 - blossom.makeRep(base);
1.437 - }
1.438 - break;
1.439 - case C:
1.440 - if ( _mate[y]!=INVALID ) { //grow
1.441 -
1.442 - ear.set(y,x);
1.443 - Node w=_mate[y];
1.444 - blossom.insert(w);
1.445 - position.set(y,A);
1.446 - position.set(w,D);
1.447 - tree.insert(y);
1.448 - tree.insert(w);
1.449 - tree.join(y,blossom.find(x));
1.450 - tree.join(w,y);
1.451 - Q.push(w);
1.452 - } else { //augment
1.453 - augment(x, ear, blossom, tree);
1.454 - _mate.set(x,y);
1.455 - _mate.set(y,x);
1.456 - return;
1.457 - } //if
1.458 - break;
1.459 - default: break;
1.460 - }
1.461 - }
1.462 - }
1.463 - }
1.464 -
1.465 - template <typename Graph>
1.466 - void MaxMatching<Graph>::greedyMatching() {
1.467 - for(NodeIt v(g); v!=INVALID; ++v)
1.468 - if ( _mate[v]==INVALID ) {
1.469 - for( IncEdgeIt e(g,v); e!=INVALID ; ++e ) {
1.470 - Node y=g.runningNode(e);
1.471 - if ( _mate[y]==INVALID && y!=v ) {
1.472 - _mate.set(v,y);
1.473 - _mate.set(y,v);
1.474 - break;
1.475 - }
1.476 - }
1.477 - }
1.478 - }
1.479 -
1.480 - template <typename Graph>
1.481 - int MaxMatching<Graph>::size() const {
1.482 - int s=0;
1.483 - for(NodeIt v(g); v!=INVALID; ++v) {
1.484 - if ( _mate[v]!=INVALID ) {
1.485 - ++s;
1.486 - }
1.487 - }
1.488 - return s/2;
1.489 - }
1.490 -
1.491 - template <typename Graph>
1.492 - void MaxMatching<Graph>::resetMatching() {
1.493 - for(NodeIt v(g); v!=INVALID; ++v)
1.494 - _mate.set(v,INVALID);
1.495 - }
1.496 -
1.497 - template <typename Graph>
1.498 - bool MaxMatching<Graph>::noShrinkStep(Node x,
1.499 - typename Graph::template
1.500 - NodeMap<Node>& ear,
1.501 - UFE& blossom, UFE& tree,
1.502 - std::queue<Node>& Q) {
1.503 - for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
1.504 - Node y=g.runningNode(e);
1.505 -
1.506 - if ( position[y]==C ) {
1.507 - if ( _mate[y]!=INVALID ) { //grow
1.508 - ear.set(y,x);
1.509 - Node w=_mate[y];
1.510 - blossom.insert(w);
1.511 - position.set(y,A);
1.512 - position.set(w,D);
1.513 - tree.insert(y);
1.514 - tree.insert(w);
1.515 - tree.join(y,blossom.find(x));
1.516 - tree.join(w,y);
1.517 - Q.push(w);
1.518 - } else { //augment
1.519 - augment(x, ear, blossom, tree);
1.520 - _mate.set(x,y);
1.521 - _mate.set(y,x);
1.522 - return true;
1.523 - }
1.524 - }
1.525 - }
1.526 - return false;
1.527 - }
1.528 -
1.529 - template <typename Graph>
1.530 - void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom,
1.531 - typename Graph::template
1.532 - NodeMap<Node>& ear,
1.533 - UFE& blossom, UFE& tree,
1.534 - std::queue<Node>& Q) {
1.535 - ear.set(top,bottom);
1.536 - Node t=top;
1.537 - while ( t!=middle ) {
1.538 - Node u=_mate[t];
1.539 - t=ear[u];
1.540 - ear.set(t,u);
1.541 - }
1.542 - bottom=_mate[middle];
1.543 - position.set(bottom,D);
1.544 - Q.push(bottom);
1.545 - top=ear[bottom];
1.546 - Node oldmiddle=middle;
1.547 - middle=blossom.find(top);
1.548 - tree.erase(bottom);
1.549 - tree.erase(oldmiddle);
1.550 - blossom.insert(bottom);
1.551 - blossom.join(bottom, oldmiddle);
1.552 - blossom.join(top, oldmiddle);
1.553 - }
1.554 -
1.555 - template <typename Graph>
1.556 - void MaxMatching<Graph>::augment(Node x,
1.557 - typename Graph::template NodeMap<Node>& ear,
1.558 - UFE& blossom, UFE& tree) {
1.559 - Node v=_mate[x];
1.560 - while ( v!=INVALID ) {
1.561 -
1.562 - Node u=ear[v];
1.563 - _mate.set(v,u);
1.564 - Node tmp=v;
1.565 - v=_mate[u];
1.566 - _mate.set(u,tmp);
1.567 - }
1.568 - typename UFE::ItemIt it;
1.569 - for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {
1.570 - if ( position[it] == D ) {
1.571 - typename UFE::ItemIt b_it;
1.572 - for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {
1.573 - position.set( b_it ,C);
1.574 - }
1.575 - blossom.eraseClass(it);
1.576 - } else position.set( it ,C);
1.577 - }
1.578 - tree.eraseClass(x);
1.579 -
1.580 - }
1.581 -
1.582 - /// @}
1.583 -
1.584 -} //END OF NAMESPACE LEMON
1.585 -
1.586 -#endif //LEMON_MAX_MATCHING_H