1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/work/jacint/max_matching.h Wed May 05 17:51:56 2004 +0000
1.3 @@ -0,0 +1,568 @@
1.4 +// -*- C++ -*-
1.5 +#ifndef HUGO_MAX_MATCHING_H
1.6 +#define HUGO_MAX_MATCHING_H
1.7 +
1.8 +///\ingroup galgs
1.9 +///\file
1.10 +///\brief Maximum matching algorithm.
1.11 +
1.12 +#include <queue>
1.13 +
1.14 +#include <invalid.h>
1.15 +#include <unionfind.h>
1.16 +
1.17 +namespace hugo {
1.18 +
1.19 + /// \addtogroup galgs
1.20 + /// @{
1.21 +
1.22 + ///Maximum matching algorithms class.
1.23 +
1.24 + ///This class provides Edmonds' alternating forest matching
1.25 + ///algorithm. The starting matching (if any) can be passed to the
1.26 + ///algorithm using read-in functions \ref readNMapNode, \ref
1.27 + ///readNMapEdge or \ref readEMapBool depending on the container. The
1.28 + ///resulting maximum matching can be attained by write-out functions
1.29 + ///\ref writeNMapNode, \ref writeNMapEdge or \ref writeEMapBool
1.30 + ///depending on the preferred container.
1.31 +
1.32 + ///The dual side of a mathcing is a map of the nodes to
1.33 + ///MaxMatching::pos_enum, having values D, A and C showing the
1.34 + ///Gallai-Edmonds decomposition of the graph. The nodes in D induce
1.35 + ///a graph with factor-critical components, the nodes in A form the
1.36 + ///barrier, and the nodes in C induce a graph having a perfect
1.37 + ///matching. This decomposition can be attained by calling \ref
1.38 + ///writePos after running the algorithm. Before subsequent runs,
1.39 + ///the function \ref resetPos() must be called.
1.40 +
1.41 + ///\param Graph The undirected graph type the algorithm runs on.
1.42 +
1.43 + ///\author Jacint Szabo
1.44 + template <typename Graph>
1.45 + class MaxMatching {
1.46 + typedef typename Graph::Node Node;
1.47 + typedef typename Graph::Edge Edge;
1.48 + typedef typename Graph::EdgeIt EdgeIt;
1.49 + typedef typename Graph::NodeIt NodeIt;
1.50 + typedef typename Graph::OutEdgeIt OutEdgeIt;
1.51 +
1.52 + typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;
1.53 +
1.54 + public:
1.55 +
1.56 + ///Indicates the Gallai-Edmonds decomposition of the graph.
1.57 +
1.58 + ///Indicates the Gallai-Edmonds decomposition of the graph, which
1.59 + ///shows an upper bound on the size of a maximum matching. The
1.60 + ///nodes with pos_enum D induce a graph with factor-critical
1.61 + ///components, the nodes in A form the canonical barrier, and the
1.62 + ///nodes in C induce a graph having a perfect matching.
1.63 + enum pos_enum {
1.64 + D=0,
1.65 + A=1,
1.66 + C=2
1.67 + };
1.68 +
1.69 + private:
1.70 +
1.71 + const Graph& G;
1.72 + typename Graph::template NodeMap<Node> mate;
1.73 + typename Graph::template NodeMap<pos_enum> position;
1.74 +
1.75 + public:
1.76 +
1.77 + MaxMatching(Graph& _G) : G(_G), mate(_G,INVALID), position(_G,C) {}
1.78 +
1.79 + ///Runs Edmonds' algorithm.
1.80 +
1.81 + ///Runs Edmonds' algorithm for sparse graphs (edgeNum >=
1.82 + ///2*nodeNum), and a heuristical Edmonds' algorithm with a
1.83 + ///heuristic of postponing shrinks for dense graphs. \pre Before
1.84 + ///the subsequent calls \ref resetPos must be called.
1.85 + void run();
1.86 +
1.87 + ///Runs Edmonds' algorithm.
1.88 +
1.89 + ///If heur=0 it runs Edmonds' algorithm. If heur=1 it runs
1.90 + ///Edmonds' algorithm with a heuristic of postponing shrinks,
1.91 + ///giving a faster algorithm for dense graphs. \pre Before the
1.92 + ///subsequent calls \ref resetPos must be called.
1.93 + void runEdmonds( int heur );
1.94 +
1.95 + ///Finds a greedy matching starting from the actual matching.
1.96 +
1.97 + ///Starting form the actual matching stored, it finds a maximal
1.98 + ///greedy matching.
1.99 + void greedyMatching();
1.100 +
1.101 + ///Returns the size of the actual matching stored.
1.102 +
1.103 + ///Returns the size of the actual matching stored. After \ref
1.104 + ///run() it returns the size of a maximum matching in the graph.
1.105 + int size();
1.106 +
1.107 + ///Resets the map storing the Gallai-Edmonds decomposition.
1.108 +
1.109 + ///Resets the map storing the Gallai-Edmonds decomposition of the
1.110 + ///graph, making it possible to run the algorithm. Must be called
1.111 + ///before all runs of the Edmonds algorithm, except for the first
1.112 + ///run.
1.113 + void resetPos();
1.114 +
1.115 + ///Resets the actual matching to the empty matching.
1.116 +
1.117 + ///Resets the actual matching to the empty matching.
1.118 + ///
1.119 + void resetMatching();
1.120 +
1.121 + ///Reads a matching from a \c Node map of \c Nodes.
1.122 +
1.123 + ///Reads a matching from a \c Node map of \c Nodes. This map must be \e
1.124 + ///symmetric, i.e. if \c map[u]=v then \c map[v]=u must hold, and
1.125 + ///now \c uv is an edge of the matching.
1.126 + template<typename NMapN>
1.127 + void readNMapNode(NMapN& map) {
1.128 + NodeIt v;
1.129 + for( G.first(v); G.valid(v); G.next(v)) {
1.130 + mate.set(v,map[v]);
1.131 + }
1.132 + }
1.133 +
1.134 + ///Writes the stored matching to a \c Node map of \c Nodes.
1.135 +
1.136 + ///Writes the stored matching to a \c Node map of \c Nodes. The
1.137 + ///resulting map will be \e symmetric, i.e. if \c map[u]=v then \c
1.138 + ///map[v]=u will hold, and now \c uv is an edge of the matching.
1.139 + template<typename NMapN>
1.140 + void writeNMapNode(NMapN& map) {
1.141 + NodeIt v;
1.142 + for( G.first(v); G.valid(v); G.next(v)) {
1.143 + map.set(v,mate[v]);
1.144 + }
1.145 + }
1.146 +
1.147 + ///Reads a matching from a \c Node map of \c Edges.
1.148 +
1.149 + ///Reads a matching from a \c Node map of incident \c Edges. This
1.150 + ///map must have the property that if \c G.bNode(map[u])=v then \c
1.151 + ///G.bNode(map[v])=u must hold, and now this edge is an edge of
1.152 + ///the matching.
1.153 + template<typename NMapE>
1.154 + void readNMapEdge(NMapE& map) {
1.155 + NodeIt v;
1.156 + for( G.first(v); G.valid(v); G.next(v)) {
1.157 + Edge e=map[v];
1.158 + if ( G.valid(e) )
1.159 + G.tail(e) == v ? mate.set(v,G.head(e)) : mate.set(v,G.tail(e));
1.160 + }
1.161 + }
1.162 +
1.163 + ///Writes the matching stored to a \c Node map of \c Edges.
1.164 +
1.165 + ///Writes the stored matching to a \c Node map of incident \c
1.166 + ///Edges. This map will have the property that if \c
1.167 + ///G.bNode(map[u])=v then \c G.bNode(map[v])=u holds, and now this
1.168 + ///edge is an edge of the matching.
1.169 + template<typename NMapE>
1.170 + void writeNMapEdge(NMapE& map) {
1.171 + typename Graph::template NodeMap<bool> todo(G,false);
1.172 + NodeIt v;
1.173 + for( G.first(v); G.valid(v); G.next(v)) {
1.174 + if ( mate[v]!=INVALID ) todo.set(v,true);
1.175 + }
1.176 + NodeIt e;
1.177 + for( G.first(e); G.valid(e); G.next(e)) {
1.178 + if ( todo[G.head(e)] && todo[G.tail(e)] ) {
1.179 + Node u=G.tail(e);
1.180 + Node v=G.head(e);
1.181 + if ( mate[u]=v && mate[v]=u ) {
1.182 + map.set(u,e);
1.183 + map.set(v,e);
1.184 + todo.set(u,false);
1.185 + todo.set(v,false);
1.186 + }
1.187 + }
1.188 + }
1.189 + }
1.190 +
1.191 + ///Reads a matching from an \c Edge map of \c bools.
1.192 +
1.193 + ///Reads a matching from an \c Edge map of \c bools. This map must
1.194 + ///have the property that there are no two adjacent edges \c e, \c
1.195 + ///f with \c map[e]=map[f]=true. The edges \c e with \c
1.196 + ///map[e]=true form the matching.
1.197 + template<typename EMapB>
1.198 + void readEMapBool(EMapB& map) {
1.199 + EdgeIt e;
1.200 + for( G.first(e); G.valid(e); G.next(e)) {
1.201 + if ( G.valid(e) ) {
1.202 + Node u=G.tail(e);
1.203 + Node v=G.head(e);
1.204 + mate.set(u,v);
1.205 + mate.set(v,u);
1.206 + }
1.207 + }
1.208 + }
1.209 +
1.210 +
1.211 + ///Writes the matching stored to an \c Edge map of \c bools.
1.212 +
1.213 + ///Writes the matching stored to an \c Edge map of \c bools. This
1.214 + ///map will have the property that there are no two adjacent edges
1.215 + ///\c e, \c f with \c map[e]=map[f]=true. The edges \c e with \c
1.216 + ///map[e]=true form the matching.
1.217 + template<typename EMapB>
1.218 + void writeEMapBool(EMapB& map) {
1.219 + typename Graph::template NodeMap<bool> todo(G,false);
1.220 + NodeIt v;
1.221 + for( G.first(v); G.valid(v); G.next(v)) {
1.222 + if ( mate[v]!=INVALID ) todo.set(v,true);
1.223 + }
1.224 +
1.225 + NodeIt e;
1.226 + for( G.first(e); G.valid(e); G.next(e)) {
1.227 + map.set(e,false);
1.228 + if ( todo[G.head(e)] && todo[G.tail(e)] ) {
1.229 + Node u=G.tail(e);
1.230 + Node v=G.head(e);
1.231 + if ( mate[u]=v && mate[v]=u ) {
1.232 + map.set(e,true);
1.233 + todo.set(u,false);
1.234 + todo.set(v,false);
1.235 + }
1.236 + }
1.237 + }
1.238 + }
1.239 +
1.240 + ///Writes the canonical decomposition of the graph after running
1.241 + ///the algorithm.
1.242 +
1.243 + ///After calling any run methods of the class, and before calling
1.244 + ///\ref resetPos(), it writes the Gallai-Edmonds canonical
1.245 + ///decomposition of the graph. \c map must be a node map of \ref pos_enum 's.
1.246 + template<typename NMapEnum>
1.247 + void writePos(NMapEnum& map) {
1.248 + NodeIt v;
1.249 + for( G.first(v); G.valid(v); G.next(v)) map.set(v,position[v]);
1.250 + }
1.251 +
1.252 + private:
1.253 +
1.254 + void lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.255 + UFE& blossom, UFE& tree);
1.256 +
1.257 + void normShrink(Node v, typename Graph::NodeMap<Node>& ear,
1.258 + UFE& blossom, UFE& tree);
1.259 +
1.260 + bool noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,
1.261 + UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.262 +
1.263 + void shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,
1.264 + UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.265 +
1.266 + void augment(Node x, typename Graph::NodeMap<Node>& ear,
1.267 + UFE& blossom, UFE& tree);
1.268 +
1.269 + };
1.270 +
1.271 +
1.272 + // **********************************************************************
1.273 + // IMPLEMENTATIONS
1.274 + // **********************************************************************
1.275 +
1.276 +
1.277 + template <typename Graph>
1.278 + void MaxMatching<Graph>::run() {
1.279 + if ( G.edgeNum() > 2*G.nodeNum() ) {
1.280 + greedyMatching();
1.281 + runEdmonds(1);
1.282 + } else runEdmonds(0);
1.283 + }
1.284 +
1.285 + template <typename Graph>
1.286 + void MaxMatching<Graph>::runEdmonds( int heur=1 ) {
1.287 +
1.288 + typename Graph::template NodeMap<Node> ear(G,INVALID);
1.289 + //undefined for the base nodes of the blossoms (i.e. for the
1.290 + //representative elements of UFE blossom) and for the nodes in C
1.291 +
1.292 + typename UFE::MapType blossom_base(G);
1.293 + UFE blossom(blossom_base);
1.294 + typename UFE::MapType tree_base(G);
1.295 + UFE tree(tree_base);
1.296 +
1.297 + NodeIt v;
1.298 + for( G.first(v); G.valid(v); G.next(v) ) {
1.299 + if ( position[v]==C && mate[v]==INVALID ) {
1.300 + blossom.insert(v);
1.301 + tree.insert(v);
1.302 + position.set(v,D);
1.303 + if ( heur == 1 ) lateShrink( v, ear, blossom, tree );
1.304 + else normShrink( v, ear, blossom, tree );
1.305 + }
1.306 + }
1.307 + }
1.308 +
1.309 + template <typename Graph>
1.310 + void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.311 + UFE& blossom, UFE& tree) {
1.312 +
1.313 + std::queue<Node> Q; //queue of the totally unscanned nodes
1.314 + Q.push(v);
1.315 + std::queue<Node> R;
1.316 + //queue of the nodes which must be scanned for a possible shrink
1.317 +
1.318 + while ( !Q.empty() ) {
1.319 + Node x=Q.front();
1.320 + Q.pop();
1.321 + if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
1.322 + else R.push(x);
1.323 + }
1.324 +
1.325 + while ( !R.empty() ) {
1.326 + Node x=R.front();
1.327 + R.pop();
1.328 +
1.329 + OutEdgeIt e;
1.330 + for( G.first(e,x); G.valid(e); G.next(e) ) {
1.331 + Node y=G.bNode(e);
1.332 +
1.333 + if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
1.334 + //x and y must be in the same tree
1.335 +
1.336 + typename Graph::template NodeMap<bool> path(G,false);
1.337 +
1.338 + Node b=blossom.find(x);
1.339 + path.set(b,true);
1.340 + b=mate[b];
1.341 + while ( b!=INVALID ) {
1.342 + b=blossom.find(ear[b]);
1.343 + path.set(b,true);
1.344 + b=mate[b];
1.345 + } //going till the root
1.346 +
1.347 + Node top=y;
1.348 + Node middle=blossom.find(top);
1.349 + Node bottom=x;
1.350 + while ( !path[middle] )
1.351 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.352 +
1.353 + Node base=middle;
1.354 + top=x;
1.355 + middle=blossom.find(top);
1.356 + bottom=y;
1.357 + Node blossom_base=blossom.find(base);
1.358 + while ( middle!=blossom_base )
1.359 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.360 +
1.361 + blossom.makeRep(base);
1.362 + } // if shrink is needed
1.363 +
1.364 + while ( !Q.empty() ) {
1.365 + Node x=Q.front();
1.366 + Q.pop();
1.367 + if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
1.368 + else R.push(x);
1.369 + }
1.370 + } //for e
1.371 + } // while ( !R.empty() )
1.372 + }
1.373 +
1.374 + template <typename Graph>
1.375 + void MaxMatching<Graph>::normShrink(Node v, typename Graph::NodeMap<Node>& ear,
1.376 + UFE& blossom, UFE& tree) {
1.377 +
1.378 + std::queue<Node> Q; //queue of the unscanned nodes
1.379 + Q.push(v);
1.380 + while ( !Q.empty() ) {
1.381 + Node x=Q.front();
1.382 + Q.pop();
1.383 +
1.384 + OutEdgeIt e;
1.385 + for( G.first(e,x); G.valid(e); G.next(e) ) {
1.386 + Node y=G.bNode(e);
1.387 +
1.388 + switch ( position[y] ) {
1.389 + case D: //x and y must be in the same tree
1.390 + if ( blossom.find(x) != blossom.find(y) ) { //shrink
1.391 + typename Graph::template NodeMap<bool> path(G,false);
1.392 +
1.393 + Node b=blossom.find(x);
1.394 + path.set(b,true);
1.395 + b=mate[b];
1.396 + while ( b!=INVALID ) {
1.397 + b=blossom.find(ear[b]);
1.398 + path.set(b,true);
1.399 + b=mate[b];
1.400 + } //going till the root
1.401 +
1.402 + Node top=y;
1.403 + Node middle=blossom.find(top);
1.404 + Node bottom=x;
1.405 + while ( !path[middle] )
1.406 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.407 +
1.408 + Node base=middle;
1.409 + top=x;
1.410 + middle=blossom.find(top);
1.411 + bottom=y;
1.412 + Node blossom_base=blossom.find(base);
1.413 + while ( middle!=blossom_base )
1.414 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.415 +
1.416 + blossom.makeRep(base);
1.417 + }
1.418 + break;
1.419 + case C:
1.420 + if ( mate[y]!=INVALID ) { //grow
1.421 + ear.set(y,x);
1.422 + Node w=mate[y];
1.423 + blossom.insert(w);
1.424 + position.set(y,A);
1.425 + position.set(w,D);
1.426 + tree.insert(y);
1.427 + tree.insert(w);
1.428 + tree.join(y,blossom.find(x));
1.429 + tree.join(w,y);
1.430 + Q.push(w);
1.431 + } else { //augment
1.432 + augment(x, ear, blossom, tree);
1.433 + mate.set(x,y);
1.434 + mate.set(y,x);
1.435 + return;
1.436 + } //if
1.437 + break;
1.438 + default: break;
1.439 + }
1.440 + }
1.441 + }
1.442 + }
1.443 +
1.444 + template <typename Graph>
1.445 + void MaxMatching<Graph>::greedyMatching() {
1.446 + NodeIt v;
1.447 + for( G.first(v); G.valid(v); G.next(v) )
1.448 + if ( mate[v]==INVALID ) {
1.449 + OutEdgeIt e;
1.450 + for( G.first(e,v); G.valid(e); G.next(e) ) {
1.451 + Node y=G.bNode(e);
1.452 + if ( mate[y]==INVALID && y!=v ) {
1.453 + mate.set(v,y);
1.454 + mate.set(y,v);
1.455 + break;
1.456 + }
1.457 + }
1.458 + }
1.459 + }
1.460 +
1.461 + template <typename Graph>
1.462 + int MaxMatching<Graph>::size() {
1.463 + int s=0;
1.464 + NodeIt v;
1.465 + for(G.first(v); G.valid(v); G.next(v) ) {
1.466 + if ( G.valid(mate[v]) ) {
1.467 + ++s;
1.468 + }
1.469 + }
1.470 + return (int)s/2;
1.471 + }
1.472 +
1.473 + template <typename Graph>
1.474 + void MaxMatching<Graph>::resetPos() {
1.475 + NodeIt v;
1.476 + for( G.first(v); G.valid(v); G.next(v))
1.477 + position.set(v,C);
1.478 + }
1.479 +
1.480 + template <typename Graph>
1.481 + void MaxMatching<Graph>::resetMatching() {
1.482 + NodeIt v;
1.483 + for( G.first(v); G.valid(v); G.next(v))
1.484 + mate.set(v,INVALID);
1.485 + }
1.486 +
1.487 + template <typename Graph>
1.488 + bool MaxMatching<Graph>::noShrinkStep(Node x, typename Graph::NodeMap<Node>& ear,
1.489 + UFE& blossom, UFE& tree, std::queue<Node>& Q) {
1.490 + OutEdgeIt e;
1.491 + for( G.first(e,x); G.valid(e); G.next(e) ) {
1.492 + Node y=G.bNode(e);
1.493 +
1.494 + if ( position[y]==C ) {
1.495 + if ( mate[y]!=INVALID ) { //grow
1.496 + ear.set(y,x);
1.497 + Node w=mate[y];
1.498 + blossom.insert(w);
1.499 + position.set(y,A);
1.500 + position.set(w,D);
1.501 + tree.insert(y);
1.502 + tree.insert(w);
1.503 + tree.join(y,blossom.find(x));
1.504 + tree.join(w,y);
1.505 + Q.push(w);
1.506 + } else { //augment
1.507 + augment(x, ear, blossom, tree);
1.508 + mate.set(x,y);
1.509 + mate.set(y,x);
1.510 + return true;
1.511 + }
1.512 + }
1.513 + }
1.514 + return false;
1.515 + }
1.516 +
1.517 + template <typename Graph>
1.518 + void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom, typename Graph::NodeMap<Node>& ear,
1.519 + UFE& blossom, UFE& tree, std::queue<Node>& Q) {
1.520 + ear.set(top,bottom);
1.521 + Node t=top;
1.522 + while ( t!=middle ) {
1.523 + Node u=mate[t];
1.524 + t=ear[u];
1.525 + ear.set(t,u);
1.526 + }
1.527 + bottom=mate[middle];
1.528 + position.set(bottom,D);
1.529 + Q.push(bottom);
1.530 + top=ear[bottom];
1.531 + Node oldmiddle=middle;
1.532 + middle=blossom.find(top);
1.533 + tree.erase(bottom);
1.534 + tree.erase(oldmiddle);
1.535 + blossom.insert(bottom);
1.536 + blossom.join(bottom, oldmiddle);
1.537 + blossom.join(top, oldmiddle);
1.538 + }
1.539 +
1.540 + template <typename Graph>
1.541 + void MaxMatching<Graph>::augment(Node x, typename Graph::NodeMap<Node>& ear,
1.542 + UFE& blossom, UFE& tree) {
1.543 + Node v=mate[x];
1.544 + while ( G.valid(v) ) {
1.545 +
1.546 + Node u=ear[v];
1.547 + mate.set(v,u);
1.548 + Node tmp=v;
1.549 + v=mate[u];
1.550 + mate.set(u,tmp);
1.551 + }
1.552 + typename UFE::ItemIt it;
1.553 + for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {
1.554 + if ( position[it] == D ) {
1.555 + typename UFE::ItemIt b_it;
1.556 + for (blossom.first(b_it,it); blossom.valid(b_it); blossom.next(b_it)) {
1.557 + position.set( b_it ,C);
1.558 + }
1.559 + blossom.eraseClass(it);
1.560 + } else position.set( it ,C);
1.561 + }
1.562 + tree.eraseClass(x);
1.563 + }
1.564 +
1.565 +
1.566 +
1.567 + /// @}
1.568 +
1.569 +} //END OF NAMESPACE HUGO
1.570 +
1.571 +#endif //EDMONDS_H