test/max_matching_test.cc
changeset 434 5c69a36729cb
parent 326 64ad48007fb2
child 440 88ed40ad0d4f
equal deleted inserted replaced
0:e36efcf4fd79 1:fd3b037e8976
    15  * purpose.
    15  * purpose.
    16  *
    16  *
    17  */
    17  */
    18 
    18 
    19 #include <iostream>
    19 #include <iostream>
       
    20 #include <sstream>
    20 #include <vector>
    21 #include <vector>
    21 #include <queue>
    22 #include <queue>
    22 #include <lemon/math.h>
    23 #include <lemon/math.h>
    23 #include <cstdlib>
    24 #include <cstdlib>
    24 
    25 
       
    26 #include <lemon/max_matching.h>
       
    27 #include <lemon/smart_graph.h>
       
    28 #include <lemon/lgf_reader.h>
       
    29 
    25 #include "test_tools.h"
    30 #include "test_tools.h"
    26 #include <lemon/list_graph.h>
       
    27 #include <lemon/max_matching.h>
       
    28 
    31 
    29 using namespace std;
    32 using namespace std;
    30 using namespace lemon;
    33 using namespace lemon;
    31 
    34 
       
    35 GRAPH_TYPEDEFS(SmartGraph);
       
    36 
       
    37 
       
    38 const int lgfn = 3;
       
    39 const std::string lgf[lgfn] = {
       
    40   "@nodes\n"
       
    41   "label\n"
       
    42   "0\n"
       
    43   "1\n"
       
    44   "2\n"
       
    45   "3\n"
       
    46   "4\n"
       
    47   "5\n"
       
    48   "6\n"
       
    49   "7\n"
       
    50   "@edges\n"
       
    51   "     label  weight\n"
       
    52   "7 4  0      984\n"
       
    53   "0 7  1      73\n"
       
    54   "7 1  2      204\n"
       
    55   "2 3  3      583\n"
       
    56   "2 7  4      565\n"
       
    57   "2 1  5      582\n"
       
    58   "0 4  6      551\n"
       
    59   "2 5  7      385\n"
       
    60   "1 5  8      561\n"
       
    61   "5 3  9      484\n"
       
    62   "7 5  10     904\n"
       
    63   "3 6  11     47\n"
       
    64   "7 6  12     888\n"
       
    65   "3 0  13     747\n"
       
    66   "6 1  14     310\n",
       
    67 
       
    68   "@nodes\n"
       
    69   "label\n"
       
    70   "0\n"
       
    71   "1\n"
       
    72   "2\n"
       
    73   "3\n"
       
    74   "4\n"
       
    75   "5\n"
       
    76   "6\n"
       
    77   "7\n"
       
    78   "@edges\n"
       
    79   "     label  weight\n"
       
    80   "2 5  0      710\n"
       
    81   "0 5  1      241\n"
       
    82   "2 4  2      856\n"
       
    83   "2 6  3      762\n"
       
    84   "4 1  4      747\n"
       
    85   "6 1  5      962\n"
       
    86   "4 7  6      723\n"
       
    87   "1 7  7      661\n"
       
    88   "2 3  8      376\n"
       
    89   "1 0  9      416\n"
       
    90   "6 7  10     391\n",
       
    91 
       
    92   "@nodes\n"
       
    93   "label\n"
       
    94   "0\n"
       
    95   "1\n"
       
    96   "2\n"
       
    97   "3\n"
       
    98   "4\n"
       
    99   "5\n"
       
   100   "6\n"
       
   101   "7\n"
       
   102   "@edges\n"
       
   103   "     label  weight\n"
       
   104   "6 2  0      553\n"
       
   105   "0 7  1      653\n"
       
   106   "6 3  2      22\n"
       
   107   "4 7  3      846\n"
       
   108   "7 2  4      981\n"
       
   109   "7 6  5      250\n"
       
   110   "5 2  6      539\n",
       
   111 };
       
   112 
       
   113 void checkMatching(const SmartGraph& graph,
       
   114                    const MaxMatching<SmartGraph>& mm) {
       
   115   int num = 0;
       
   116 
       
   117   IntNodeMap comp_index(graph);
       
   118   UnionFind<IntNodeMap> comp(comp_index);
       
   119 
       
   120   int barrier_num = 0;
       
   121 
       
   122   for (NodeIt n(graph); n != INVALID; ++n) {
       
   123     check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
       
   124           mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
       
   125     if (mm.decomposition(n) == MaxMatching<SmartGraph>::ODD) {
       
   126       ++barrier_num;
       
   127     } else {
       
   128       comp.insert(n);
       
   129     }
       
   130   }
       
   131 
       
   132   for (EdgeIt e(graph); e != INVALID; ++e) {
       
   133     if (mm.matching(e)) {
       
   134       check(e == mm.matching(graph.u(e)), "Wrong matching");
       
   135       check(e == mm.matching(graph.v(e)), "Wrong matching");
       
   136       ++num;
       
   137     }
       
   138     check(mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
       
   139           mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
       
   140           "Wrong Gallai-Edmonds decomposition");
       
   141 
       
   142     check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
       
   143           mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
       
   144           "Wrong Gallai-Edmonds decomposition");
       
   145 
       
   146     if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
       
   147         mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
       
   148       comp.join(graph.u(e), graph.v(e));
       
   149     }
       
   150   }
       
   151 
       
   152   std::set<int> comp_root;
       
   153   int odd_comp_num = 0;
       
   154   for (NodeIt n(graph); n != INVALID; ++n) {
       
   155     if (mm.decomposition(n) != MaxMatching<SmartGraph>::ODD) {
       
   156       int root = comp.find(n);
       
   157       if (comp_root.find(root) == comp_root.end()) {
       
   158         comp_root.insert(root);
       
   159         if (comp.size(n) % 2 == 1) {
       
   160           ++odd_comp_num;
       
   161         }
       
   162       }
       
   163     }
       
   164   }
       
   165 
       
   166   check(mm.matchingSize() == num, "Wrong matching");
       
   167   check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
       
   168          "Wrong matching");
       
   169   return;
       
   170 }
       
   171 
       
   172 void checkWeightedMatching(const SmartGraph& graph,
       
   173                    const SmartGraph::EdgeMap<int>& weight,
       
   174                    const MaxWeightedMatching<SmartGraph>& mwm) {
       
   175   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
       
   176     if (graph.u(e) == graph.v(e)) continue;
       
   177     int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
       
   178 
       
   179     for (int i = 0; i < mwm.blossomNum(); ++i) {
       
   180       bool s = false, t = false;
       
   181       for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
       
   182            n != INVALID; ++n) {
       
   183         if (graph.u(e) == n) s = true;
       
   184         if (graph.v(e) == n) t = true;
       
   185       }
       
   186       if (s == true && t == true) {
       
   187         rw += mwm.blossomValue(i);
       
   188       }
       
   189     }
       
   190     rw -= weight[e] * mwm.dualScale;
       
   191 
       
   192     check(rw >= 0, "Negative reduced weight");
       
   193     check(rw == 0 || !mwm.matching(e),
       
   194           "Non-zero reduced weight on matching edge");
       
   195   }
       
   196 
       
   197   int pv = 0;
       
   198   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
       
   199     if (mwm.matching(n) != INVALID) {
       
   200       check(mwm.nodeValue(n) >= 0, "Invalid node value");
       
   201       pv += weight[mwm.matching(n)];
       
   202       SmartGraph::Node o = graph.target(mwm.matching(n));
       
   203       check(mwm.mate(n) == o, "Invalid matching");
       
   204       check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
       
   205             "Invalid matching");
       
   206     } else {
       
   207       check(mwm.mate(n) == INVALID, "Invalid matching");
       
   208       check(mwm.nodeValue(n) == 0, "Invalid matching");
       
   209     }
       
   210   }
       
   211 
       
   212   int dv = 0;
       
   213   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
       
   214     dv += mwm.nodeValue(n);
       
   215   }
       
   216 
       
   217   for (int i = 0; i < mwm.blossomNum(); ++i) {
       
   218     check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
       
   219     check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
       
   220     dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
       
   221   }
       
   222 
       
   223   check(pv * mwm.dualScale == dv * 2, "Wrong duality");
       
   224 
       
   225   return;
       
   226 }
       
   227 
       
   228 void checkWeightedPerfectMatching(const SmartGraph& graph,
       
   229                           const SmartGraph::EdgeMap<int>& weight,
       
   230                           const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
       
   231   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
       
   232     if (graph.u(e) == graph.v(e)) continue;
       
   233     int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
       
   234 
       
   235     for (int i = 0; i < mwpm.blossomNum(); ++i) {
       
   236       bool s = false, t = false;
       
   237       for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
       
   238            n != INVALID; ++n) {
       
   239         if (graph.u(e) == n) s = true;
       
   240         if (graph.v(e) == n) t = true;
       
   241       }
       
   242       if (s == true && t == true) {
       
   243         rw += mwpm.blossomValue(i);
       
   244       }
       
   245     }
       
   246     rw -= weight[e] * mwpm.dualScale;
       
   247 
       
   248     check(rw >= 0, "Negative reduced weight");
       
   249     check(rw == 0 || !mwpm.matching(e),
       
   250           "Non-zero reduced weight on matching edge");
       
   251   }
       
   252 
       
   253   int pv = 0;
       
   254   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
       
   255     check(mwpm.matching(n) != INVALID, "Non perfect");
       
   256     pv += weight[mwpm.matching(n)];
       
   257     SmartGraph::Node o = graph.target(mwpm.matching(n));
       
   258     check(mwpm.mate(n) == o, "Invalid matching");
       
   259     check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
       
   260           "Invalid matching");
       
   261   }
       
   262 
       
   263   int dv = 0;
       
   264   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
       
   265     dv += mwpm.nodeValue(n);
       
   266   }
       
   267 
       
   268   for (int i = 0; i < mwpm.blossomNum(); ++i) {
       
   269     check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
       
   270     check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
       
   271     dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
       
   272   }
       
   273 
       
   274   check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
       
   275 
       
   276   return;
       
   277 }
       
   278 
       
   279 
    32 int main() {
   280 int main() {
    33 
   281 
    34   typedef ListGraph Graph;
   282   for (int i = 0; i < lgfn; ++i) {
    35 
   283     SmartGraph graph;
    36   GRAPH_TYPEDEFS(Graph);
   284     SmartGraph::EdgeMap<int> weight(graph);
    37 
   285 
    38   Graph g;
   286     istringstream lgfs(lgf[i]);
    39   g.clear();
   287     graphReader(graph, lgfs).
    40 
   288       edgeMap("weight", weight).run();
    41   std::vector<Graph::Node> nodes;
   289 
    42   for (int i=0; i<13; ++i)
   290     MaxMatching<SmartGraph> mm(graph);
    43       nodes.push_back(g.addNode());
   291     mm.run();
    44 
   292     checkMatching(graph, mm);
    45   g.addEdge(nodes[0], nodes[0]);
   293 
    46   g.addEdge(nodes[6], nodes[10]);
   294     MaxWeightedMatching<SmartGraph> mwm(graph, weight);
    47   g.addEdge(nodes[5], nodes[10]);
   295     mwm.run();
    48   g.addEdge(nodes[4], nodes[10]);
   296     checkWeightedMatching(graph, weight, mwm);
    49   g.addEdge(nodes[3], nodes[11]);
   297 
    50   g.addEdge(nodes[1], nodes[6]);
   298     MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
    51   g.addEdge(nodes[4], nodes[7]);
   299     bool perfect = mwpm.run();
    52   g.addEdge(nodes[1], nodes[8]);
   300 
    53   g.addEdge(nodes[0], nodes[8]);
   301     check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
    54   g.addEdge(nodes[3], nodes[12]);
   302           "Perfect matching found");
    55   g.addEdge(nodes[6], nodes[9]);
   303 
    56   g.addEdge(nodes[9], nodes[11]);
   304     if (perfect) {
    57   g.addEdge(nodes[2], nodes[10]);
   305       checkWeightedPerfectMatching(graph, weight, mwpm);
    58   g.addEdge(nodes[10], nodes[8]);
   306     }
    59   g.addEdge(nodes[5], nodes[8]);
   307   }
    60   g.addEdge(nodes[6], nodes[3]);
       
    61   g.addEdge(nodes[0], nodes[5]);
       
    62   g.addEdge(nodes[6], nodes[12]);
       
    63 
       
    64   MaxMatching<Graph> max_matching(g);
       
    65   max_matching.init();
       
    66   max_matching.startDense();
       
    67 
       
    68   int s=0;
       
    69   Graph::NodeMap<Node> mate(g,INVALID);
       
    70   max_matching.mateMap(mate);
       
    71   for(NodeIt v(g); v!=INVALID; ++v) {
       
    72     if ( mate[v]!=INVALID ) ++s;
       
    73   }
       
    74   int size=int(s/2);  //size will be used as the size of a maxmatching
       
    75 
       
    76   for(NodeIt v(g); v!=INVALID; ++v) {
       
    77     max_matching.mate(v);
       
    78   }
       
    79 
       
    80   check ( size == max_matching.size(), "mate() returns a different size matching than max_matching.size()" );
       
    81 
       
    82   Graph::NodeMap<MaxMatching<Graph>::DecompType> pos0(g);
       
    83   max_matching.decomposition(pos0);
       
    84 
       
    85   max_matching.init();
       
    86   max_matching.startSparse();
       
    87   s=0;
       
    88   max_matching.mateMap(mate);
       
    89   for(NodeIt v(g); v!=INVALID; ++v) {
       
    90     if ( mate[v]!=INVALID ) ++s;
       
    91   }
       
    92   check ( int(s/2) == size, "The size does not equal!" );
       
    93 
       
    94   Graph::NodeMap<MaxMatching<Graph>::DecompType> pos1(g);
       
    95   max_matching.decomposition(pos1);
       
    96 
       
    97   max_matching.run();
       
    98   s=0;
       
    99   max_matching.mateMap(mate);
       
   100   for(NodeIt v(g); v!=INVALID; ++v) {
       
   101     if ( mate[v]!=INVALID ) ++s;
       
   102   }
       
   103   check ( int(s/2) == size, "The size does not equal!" );
       
   104 
       
   105   Graph::NodeMap<MaxMatching<Graph>::DecompType> pos2(g);
       
   106   max_matching.decomposition(pos2);
       
   107 
       
   108   max_matching.run();
       
   109   s=0;
       
   110   max_matching.mateMap(mate);
       
   111   for(NodeIt v(g); v!=INVALID; ++v) {
       
   112     if ( mate[v]!=INVALID ) ++s;
       
   113   }
       
   114   check ( int(s/2) == size, "The size does not equal!" );
       
   115 
       
   116   Graph::NodeMap<MaxMatching<Graph>::DecompType> pos(g);
       
   117   max_matching.decomposition(pos);
       
   118 
       
   119   bool ismatching=true;
       
   120   for(NodeIt v(g); v!=INVALID; ++v) {
       
   121     if ( mate[v]!=INVALID ) {
       
   122       Node u=mate[v];
       
   123       if (mate[u]!=v) ismatching=false;
       
   124     }
       
   125   }
       
   126   check ( ismatching, "It is not a matching!" );
       
   127 
       
   128   bool coincide=true;
       
   129   for(NodeIt v(g); v!=INVALID; ++v) {
       
   130    if ( pos0[v] != pos1[v] || pos1[v]!=pos2[v] || pos2[v]!=pos[v] ) {
       
   131      coincide=false;
       
   132     }
       
   133   }
       
   134   check ( coincide, "The decompositions do not coincide! " );
       
   135 
       
   136   bool noarc=true;
       
   137   for(EdgeIt e(g); e!=INVALID; ++e) {
       
   138    if ( (pos[g.v(e)]==max_matching.C &&
       
   139          pos[g.u(e)]==max_matching.D) ||
       
   140          (pos[g.v(e)]==max_matching.D &&
       
   141           pos[g.u(e)]==max_matching.C) )
       
   142       noarc=false;
       
   143   }
       
   144   check ( noarc, "There are arcs between D and C!" );
       
   145 
       
   146   bool oddcomp=true;
       
   147   Graph::NodeMap<bool> todo(g,true);
       
   148   int num_comp=0;
       
   149   for(NodeIt v(g); v!=INVALID; ++v) {
       
   150    if ( pos[v]==max_matching.D && todo[v] ) {
       
   151       int comp_size=1;
       
   152       ++num_comp;
       
   153       std::queue<Node> Q;
       
   154       Q.push(v);
       
   155       todo.set(v,false);
       
   156       while (!Q.empty()) {
       
   157         Node w=Q.front();
       
   158         Q.pop();
       
   159         for(IncEdgeIt e(g,w); e!=INVALID; ++e) {
       
   160           Node u=g.runningNode(e);
       
   161           if ( pos[u]==max_matching.D && todo[u] ) {
       
   162             ++comp_size;
       
   163             Q.push(u);
       
   164             todo.set(u,false);
       
   165           }
       
   166         }
       
   167       }
       
   168       if ( !(comp_size % 2) ) oddcomp=false;
       
   169     }
       
   170   }
       
   171   check ( oddcomp, "A component of g[D] is not odd." );
       
   172 
       
   173   int barrier=0;
       
   174   for(NodeIt v(g); v!=INVALID; ++v) {
       
   175     if ( pos[v]==max_matching.A ) ++barrier;
       
   176   }
       
   177   int expected_size=int( countNodes(g)-num_comp+barrier)/2;
       
   178   check ( size==expected_size, "The size of the matching is wrong." );
       
   179 
   308 
   180   return 0;
   309   return 0;
   181 }
   310 }