1.1 --- a/lemon/max_matching.h Thu Mar 30 09:42:05 2006 +0000
1.2 +++ b/lemon/max_matching.h Thu Mar 30 15:02:11 2006 +0000
1.3 @@ -114,6 +114,7 @@
1.4 ///giving a faster algorithm for dense graphs.
1.5 void runEdmonds( int heur = 1 ) {
1.6
1.7 + //each vertex is put to C
1.8 for(NodeIt v(g); v!=INVALID; ++v)
1.9 position.set(v,C);
1.10
1.11 @@ -128,6 +129,11 @@
1.12 //If these UFE's would be members of the class then also
1.13 //blossom_base and tree_base should be a member.
1.14
1.15 + //We build only one tree and the other vertices uncovered by the
1.16 + //matching belong to C. (They can be considered as singleton
1.17 + //trees.) If this tree can be augmented or no more
1.18 + //grow/augmentation/shrink is possible then we return to this
1.19 + //"for" cycle.
1.20 for(NodeIt v(g); v!=INVALID; ++v) {
1.21 if ( position[v]==C && _mate[v]==INVALID ) {
1.22 blossom.insert(v);
1.23 @@ -223,8 +229,8 @@
1.24 ///joining \c u to \c v will be an edge of the matching.
1.25 template<typename NMapE>
1.26 void readNMapEdge(NMapE& map) {
1.27 - for(NodeIt v(g); v!=INVALID; ++v) {
1.28 - UEdge e=map[v];
1.29 + for(NodeIt v(g); v!=INVALID; ++v) {
1.30 + UEdge e=map[v];
1.31 if ( e!=INVALID )
1.32 _mate.set(v,g.oppositeNode(v,e));
1.33 }
1.34 @@ -323,13 +329,17 @@
1.35 void normShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.36 UFE& blossom, UFE& tree);
1.37
1.38 - bool noShrinkStep(Node x, typename Graph::template NodeMap<Node>& ear,
1.39 - UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.40 + void shrink(Node x,Node y, typename Graph::template NodeMap<Node>& ear,
1.41 + UFE& blossom, UFE& tree,std::queue<Node>& Q);
1.42
1.43 void shrinkStep(Node& top, Node& middle, Node& bottom,
1.44 typename Graph::template NodeMap<Node>& ear,
1.45 UFE& blossom, UFE& tree, std::queue<Node>& Q);
1.46
1.47 + bool growOrAugment(Node& y, Node& x, typename Graph::template
1.48 + NodeMap<Node>& ear, UFE& blossom, UFE& tree,
1.49 + std::queue<Node>& Q);
1.50 +
1.51 void augment(Node x, typename Graph::template NodeMap<Node>& ear,
1.52 UFE& blossom, UFE& tree);
1.53
1.54 @@ -342,8 +352,11 @@
1.55
1.56
1.57 template <typename Graph>
1.58 - void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template NodeMap<Node>& ear,
1.59 - UFE& blossom, UFE& tree) {
1.60 + void MaxMatching<Graph>::lateShrink(Node v, typename Graph::template
1.61 + NodeMap<Node>& ear, UFE& blossom, UFE& tree) {
1.62 + //We have one tree which we grow, and also shrink but only if it cannot be
1.63 + //postponed. If we augment then we return to the "for" cycle of
1.64 + //runEdmonds().
1.65
1.66 std::queue<Node> Q; //queue of the totally unscanned nodes
1.67 Q.push(v);
1.68 @@ -353,8 +366,13 @@
1.69 while ( !Q.empty() ) {
1.70 Node x=Q.front();
1.71 Q.pop();
1.72 - if ( noShrinkStep( x, ear, blossom, tree, Q ) ) return;
1.73 - else R.push(x);
1.74 + for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
1.75 + Node y=g.runningNode(e);
1.76 + //growOrAugment grows if y is covered by the matching and
1.77 + //augments if not. In this latter case it returns 1.
1.78 + if ( position[y]==C && growOrAugment(y, x, ear, blossom, tree, Q) ) return;
1.79 + }
1.80 + R.push(x);
1.81 }
1.82
1.83 while ( !R.empty() ) {
1.84 @@ -364,42 +382,20 @@
1.85 for( IncEdgeIt e(g,x); e!=INVALID ; ++e ) {
1.86 Node y=g.runningNode(e);
1.87
1.88 - if ( position[y] == D && blossom.find(x) != blossom.find(y) ) {
1.89 - //x and y must be in the same tree
1.90 + if ( position[y] == D && blossom.find(x) != blossom.find(y) )
1.91 + //Recall that we have only one tree.
1.92 + shrink( x, y, ear, blossom, tree, Q);
1.93
1.94 - typename Graph::template NodeMap<bool> path(g,false);
1.95 -
1.96 - Node b=blossom.find(x);
1.97 - path.set(b,true);
1.98 - b=_mate[b];
1.99 - while ( b!=INVALID ) {
1.100 - b=blossom.find(ear[b]);
1.101 - path.set(b,true);
1.102 - b=_mate[b];
1.103 - } //going till the root
1.104 -
1.105 - Node top=y;
1.106 - Node middle=blossom.find(top);
1.107 - Node bottom=x;
1.108 - while ( !path[middle] )
1.109 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.110 -
1.111 - Node base=middle;
1.112 - top=x;
1.113 - middle=blossom.find(top);
1.114 - bottom=y;
1.115 - Node blossom_base=blossom.find(base);
1.116 - while ( middle!=blossom_base )
1.117 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.118 -
1.119 - blossom.makeRep(base);
1.120 - } // if shrink is needed
1.121 -
1.122 while ( !Q.empty() ) {
1.123 Node x=Q.front();
1.124 Q.pop();
1.125 - if ( noShrinkStep(x, ear, blossom, tree, Q) ) return;
1.126 - else R.push(x);
1.127 + for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
1.128 + Node y=g.runningNode(e);
1.129 + //growOrAugment grows if y is covered by the matching and
1.130 + //augments if not. In this latter case it returns 1.
1.131 + if ( position[y]==C && growOrAugment(y, x, ear, blossom, tree, Q) ) return;
1.132 + }
1.133 + R.push(x);
1.134 }
1.135 } //for e
1.136 } // while ( !R.empty() )
1.137 @@ -411,6 +407,9 @@
1.138 typename Graph::template
1.139 NodeMap<Node>& ear,
1.140 UFE& blossom, UFE& tree) {
1.141 + //We have one tree, which we grow and shrink. If we augment then we
1.142 + //return to the "for" cycle of runEdmonds().
1.143 +
1.144 std::queue<Node> Q; //queue of the unscanned nodes
1.145 Q.push(v);
1.146 while ( !Q.empty() ) {
1.147 @@ -423,100 +422,70 @@
1.148
1.149 switch ( position[y] ) {
1.150 case D: //x and y must be in the same tree
1.151 -
1.152 - if ( blossom.find(x) != blossom.find(y) ) { //shrink
1.153 - typename Graph::template NodeMap<bool> path(g,false);
1.154 -
1.155 - Node b=blossom.find(x);
1.156 - path.set(b,true);
1.157 - b=_mate[b];
1.158 - while ( b!=INVALID ) {
1.159 - b=blossom.find(ear[b]);
1.160 - path.set(b,true);
1.161 - b=_mate[b];
1.162 - } //going till the root
1.163 -
1.164 - Node top=y;
1.165 - Node middle=blossom.find(top);
1.166 - Node bottom=x;
1.167 - while ( !path[middle] )
1.168 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.169 -
1.170 - Node base=middle;
1.171 - top=x;
1.172 - middle=blossom.find(top);
1.173 - bottom=y;
1.174 - Node blossom_base=blossom.find(base);
1.175 - while ( middle!=blossom_base )
1.176 - shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.177 -
1.178 - blossom.makeRep(base);
1.179 - }
1.180 + if ( blossom.find(x) != blossom.find(y) )
1.181 + //x and y are in the same tree
1.182 + shrink( x, y, ear, blossom, tree, Q);
1.183 break;
1.184 case C:
1.185 - if ( _mate[y]!=INVALID ) { //grow
1.186 -
1.187 - ear.set(y,x);
1.188 - Node w=_mate[y];
1.189 - blossom.insert(w);
1.190 - position.set(y,A);
1.191 - position.set(w,D);
1.192 - tree.insert(y);
1.193 - tree.insert(w);
1.194 - tree.join(y,blossom.find(x));
1.195 - tree.join(w,y);
1.196 - Q.push(w);
1.197 - } else { //augment
1.198 - augment(x, ear, blossom, tree);
1.199 - _mate.set(x,y);
1.200 - _mate.set(y,x);
1.201 - return;
1.202 - } //if
1.203 + //growOrAugment grows if y is covered by the matching and
1.204 + //augments if not. In this latter case it returns 1.
1.205 + if ( growOrAugment(y, x, ear, blossom, tree, Q) ) return;
1.206 break;
1.207 default: break;
1.208 - }
1.209 + }
1.210 }
1.211 }
1.212 }
1.213 +
1.214
1.215 template <typename Graph>
1.216 - bool MaxMatching<Graph>::noShrinkStep(Node x,
1.217 - typename Graph::template
1.218 - NodeMap<Node>& ear,
1.219 - UFE& blossom, UFE& tree,
1.220 - std::queue<Node>& Q) {
1.221 - for( IncEdgeIt e(g,x); e!= INVALID; ++e ) {
1.222 - Node y=g.runningNode(e);
1.223 -
1.224 - if ( position[y]==C ) {
1.225 - if ( _mate[y]!=INVALID ) { //grow
1.226 - ear.set(y,x);
1.227 - Node w=_mate[y];
1.228 - blossom.insert(w);
1.229 - position.set(y,A);
1.230 - position.set(w,D);
1.231 - tree.insert(y);
1.232 - tree.insert(w);
1.233 - tree.join(y,blossom.find(x));
1.234 - tree.join(w,y);
1.235 - Q.push(w);
1.236 - } else { //augment
1.237 - augment(x, ear, blossom, tree);
1.238 - _mate.set(x,y);
1.239 - _mate.set(y,x);
1.240 - return true;
1.241 - }
1.242 - }
1.243 - }
1.244 - return false;
1.245 + void MaxMatching<Graph>::shrink(Node x,Node y, typename
1.246 + Graph::template NodeMap<Node>& ear,
1.247 + UFE& blossom, UFE& tree, std::queue<Node>& Q) {
1.248 + //x and y are the two adjacent vertices in two blossoms.
1.249 +
1.250 + typename Graph::template NodeMap<bool> path(g,false);
1.251 +
1.252 + Node b=blossom.find(x);
1.253 + path.set(b,true);
1.254 + b=_mate[b];
1.255 + while ( b!=INVALID ) {
1.256 + b=blossom.find(ear[b]);
1.257 + path.set(b,true);
1.258 + b=_mate[b];
1.259 + } //we go until the root through bases of blossoms and odd vertices
1.260 +
1.261 + Node top=y;
1.262 + Node middle=blossom.find(top);
1.263 + Node bottom=x;
1.264 + while ( !path[middle] )
1.265 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.266 + //Until we arrive to a node on the path, we update blossom, tree
1.267 + //and the positions of the odd nodes.
1.268 +
1.269 + Node base=middle;
1.270 + top=x;
1.271 + middle=blossom.find(top);
1.272 + bottom=y;
1.273 + Node blossom_base=blossom.find(base);
1.274 + while ( middle!=blossom_base )
1.275 + shrinkStep(top, middle, bottom, ear, blossom, tree, Q);
1.276 + //Until we arrive to a node on the path, we update blossom, tree
1.277 + //and the positions of the odd nodes.
1.278 +
1.279 + blossom.makeRep(base);
1.280 }
1.281
1.282 +
1.283 +
1.284 template <typename Graph>
1.285 void MaxMatching<Graph>::shrinkStep(Node& top, Node& middle, Node& bottom,
1.286 typename Graph::template
1.287 NodeMap<Node>& ear,
1.288 UFE& blossom, UFE& tree,
1.289 std::queue<Node>& Q) {
1.290 + //We traverse a blossom and update everything.
1.291 +
1.292 ear.set(top,bottom);
1.293 Node t=top;
1.294 while ( t!=middle ) {
1.295 @@ -537,6 +506,36 @@
1.296 blossom.join(top, oldmiddle);
1.297 }
1.298
1.299 +
1.300 + template <typename Graph>
1.301 + bool MaxMatching<Graph>::growOrAugment(Node& y, Node& x, typename Graph::template
1.302 + NodeMap<Node>& ear, UFE& blossom, UFE& tree,
1.303 + std::queue<Node>& Q) {
1.304 + //x is in a blossom in the tree, y is outside. If y is covered by
1.305 + //the matching we grow, otherwise we augment. In this case we
1.306 + //return 1.
1.307 +
1.308 + if ( _mate[y]!=INVALID ) { //grow
1.309 + ear.set(y,x);
1.310 + Node w=_mate[y];
1.311 + blossom.insert(w);
1.312 + position.set(y,A);
1.313 + position.set(w,D);
1.314 + tree.insert(y);
1.315 + tree.insert(w);
1.316 + tree.join(y,blossom.find(x));
1.317 + tree.join(w,y);
1.318 + Q.push(w);
1.319 + } else { //augment
1.320 + augment(x, ear, blossom, tree);
1.321 + _mate.set(x,y);
1.322 + _mate.set(y,x);
1.323 + return true;
1.324 + }
1.325 + return false;
1.326 + }
1.327 +
1.328 +
1.329 template <typename Graph>
1.330 void MaxMatching<Graph>::augment(Node x,
1.331 typename Graph::template NodeMap<Node>& ear,
1.332 @@ -550,6 +549,7 @@
1.333 v=_mate[u];
1.334 _mate.set(u,tmp);
1.335 }
1.336 + Node y=blossom.find(x);
1.337 typename UFE::ItemIt it;
1.338 for (tree.first(it,blossom.find(x)); tree.valid(it); tree.next(it)) {
1.339 if ( position[it] == D ) {
1.340 @@ -560,7 +560,7 @@
1.341 blossom.eraseClass(it);
1.342 } else position.set( it ,C);
1.343 }
1.344 - tree.eraseClass(x);
1.345 + tree.eraseClass(y);
1.346
1.347 }
1.348