test/matching_test.cc
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 17 Apr 2009 09:58:50 +0200
changeset 594 d657c71db7db
parent 593 test/max_matching_test.cc@7ac52d6a268e
child 870 61120524af27
child 969 7e368d9b67f7
permissions -rw-r--r--
Rename max_matching.h to matching.h (#265)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #include <iostream>
    20 #include <sstream>
    21 #include <vector>
    22 #include <queue>
    23 #include <cstdlib>
    24 
    25 #include <lemon/matching.h>
    26 #include <lemon/smart_graph.h>
    27 #include <lemon/concepts/graph.h>
    28 #include <lemon/concepts/maps.h>
    29 #include <lemon/lgf_reader.h>
    30 #include <lemon/math.h>
    31 
    32 #include "test_tools.h"
    33 
    34 using namespace std;
    35 using namespace lemon;
    36 
    37 GRAPH_TYPEDEFS(SmartGraph);
    38 
    39 
    40 const int lgfn = 3;
    41 const std::string lgf[lgfn] = {
    42   "@nodes\n"
    43   "label\n"
    44   "0\n"
    45   "1\n"
    46   "2\n"
    47   "3\n"
    48   "4\n"
    49   "5\n"
    50   "6\n"
    51   "7\n"
    52   "@edges\n"
    53   "     label  weight\n"
    54   "7 4  0      984\n"
    55   "0 7  1      73\n"
    56   "7 1  2      204\n"
    57   "2 3  3      583\n"
    58   "2 7  4      565\n"
    59   "2 1  5      582\n"
    60   "0 4  6      551\n"
    61   "2 5  7      385\n"
    62   "1 5  8      561\n"
    63   "5 3  9      484\n"
    64   "7 5  10     904\n"
    65   "3 6  11     47\n"
    66   "7 6  12     888\n"
    67   "3 0  13     747\n"
    68   "6 1  14     310\n",
    69 
    70   "@nodes\n"
    71   "label\n"
    72   "0\n"
    73   "1\n"
    74   "2\n"
    75   "3\n"
    76   "4\n"
    77   "5\n"
    78   "6\n"
    79   "7\n"
    80   "@edges\n"
    81   "     label  weight\n"
    82   "2 5  0      710\n"
    83   "0 5  1      241\n"
    84   "2 4  2      856\n"
    85   "2 6  3      762\n"
    86   "4 1  4      747\n"
    87   "6 1  5      962\n"
    88   "4 7  6      723\n"
    89   "1 7  7      661\n"
    90   "2 3  8      376\n"
    91   "1 0  9      416\n"
    92   "6 7  10     391\n",
    93 
    94   "@nodes\n"
    95   "label\n"
    96   "0\n"
    97   "1\n"
    98   "2\n"
    99   "3\n"
   100   "4\n"
   101   "5\n"
   102   "6\n"
   103   "7\n"
   104   "@edges\n"
   105   "     label  weight\n"
   106   "6 2  0      553\n"
   107   "0 7  1      653\n"
   108   "6 3  2      22\n"
   109   "4 7  3      846\n"
   110   "7 2  4      981\n"
   111   "7 6  5      250\n"
   112   "5 2  6      539\n",
   113 };
   114 
   115 void checkMaxMatchingCompile()
   116 {
   117   typedef concepts::Graph Graph;
   118   typedef Graph::Node Node;
   119   typedef Graph::Edge Edge;
   120   typedef Graph::EdgeMap<bool> MatMap;
   121 
   122   Graph g;
   123   Node n;
   124   Edge e;
   125   MatMap mat(g);
   126 
   127   MaxMatching<Graph> mat_test(g);
   128   const MaxMatching<Graph>&
   129     const_mat_test = mat_test;
   130 
   131   mat_test.init();
   132   mat_test.greedyInit();
   133   mat_test.matchingInit(mat);
   134   mat_test.startSparse();
   135   mat_test.startDense();
   136   mat_test.run();
   137   
   138   const_mat_test.matchingSize();
   139   const_mat_test.matching(e);
   140   const_mat_test.matching(n);
   141   const MaxMatching<Graph>::MatchingMap& mmap =
   142     const_mat_test.matchingMap();
   143   e = mmap[n];
   144   const_mat_test.mate(n);
   145 
   146   MaxMatching<Graph>::Status stat = 
   147     const_mat_test.status(n);
   148   const MaxMatching<Graph>::StatusMap& smap =
   149     const_mat_test.statusMap();
   150   stat = smap[n];
   151   const_mat_test.barrier(n);
   152 }
   153 
   154 void checkMaxWeightedMatchingCompile()
   155 {
   156   typedef concepts::Graph Graph;
   157   typedef Graph::Node Node;
   158   typedef Graph::Edge Edge;
   159   typedef Graph::EdgeMap<int> WeightMap;
   160 
   161   Graph g;
   162   Node n;
   163   Edge e;
   164   WeightMap w(g);
   165 
   166   MaxWeightedMatching<Graph> mat_test(g, w);
   167   const MaxWeightedMatching<Graph>&
   168     const_mat_test = mat_test;
   169 
   170   mat_test.init();
   171   mat_test.start();
   172   mat_test.run();
   173   
   174   const_mat_test.matchingWeight();
   175   const_mat_test.matchingSize();
   176   const_mat_test.matching(e);
   177   const_mat_test.matching(n);
   178   const MaxWeightedMatching<Graph>::MatchingMap& mmap =
   179     const_mat_test.matchingMap();
   180   e = mmap[n];
   181   const_mat_test.mate(n);
   182   
   183   int k = 0;
   184   const_mat_test.dualValue();
   185   const_mat_test.nodeValue(n);
   186   const_mat_test.blossomNum();
   187   const_mat_test.blossomSize(k);
   188   const_mat_test.blossomValue(k);
   189 }
   190 
   191 void checkMaxWeightedPerfectMatchingCompile()
   192 {
   193   typedef concepts::Graph Graph;
   194   typedef Graph::Node Node;
   195   typedef Graph::Edge Edge;
   196   typedef Graph::EdgeMap<int> WeightMap;
   197 
   198   Graph g;
   199   Node n;
   200   Edge e;
   201   WeightMap w(g);
   202 
   203   MaxWeightedPerfectMatching<Graph> mat_test(g, w);
   204   const MaxWeightedPerfectMatching<Graph>&
   205     const_mat_test = mat_test;
   206 
   207   mat_test.init();
   208   mat_test.start();
   209   mat_test.run();
   210   
   211   const_mat_test.matchingWeight();
   212   const_mat_test.matching(e);
   213   const_mat_test.matching(n);
   214   const MaxWeightedPerfectMatching<Graph>::MatchingMap& mmap =
   215     const_mat_test.matchingMap();
   216   e = mmap[n];
   217   const_mat_test.mate(n);
   218   
   219   int k = 0;
   220   const_mat_test.dualValue();
   221   const_mat_test.nodeValue(n);
   222   const_mat_test.blossomNum();
   223   const_mat_test.blossomSize(k);
   224   const_mat_test.blossomValue(k);
   225 }
   226 
   227 void checkMatching(const SmartGraph& graph,
   228                    const MaxMatching<SmartGraph>& mm) {
   229   int num = 0;
   230 
   231   IntNodeMap comp_index(graph);
   232   UnionFind<IntNodeMap> comp(comp_index);
   233 
   234   int barrier_num = 0;
   235 
   236   for (NodeIt n(graph); n != INVALID; ++n) {
   237     check(mm.status(n) == MaxMatching<SmartGraph>::EVEN ||
   238           mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
   239     if (mm.status(n) == MaxMatching<SmartGraph>::ODD) {
   240       ++barrier_num;
   241     } else {
   242       comp.insert(n);
   243     }
   244   }
   245 
   246   for (EdgeIt e(graph); e != INVALID; ++e) {
   247     if (mm.matching(e)) {
   248       check(e == mm.matching(graph.u(e)), "Wrong matching");
   249       check(e == mm.matching(graph.v(e)), "Wrong matching");
   250       ++num;
   251     }
   252     check(mm.status(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
   253           mm.status(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
   254           "Wrong Gallai-Edmonds decomposition");
   255 
   256     check(mm.status(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
   257           mm.status(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
   258           "Wrong Gallai-Edmonds decomposition");
   259 
   260     if (mm.status(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
   261         mm.status(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
   262       comp.join(graph.u(e), graph.v(e));
   263     }
   264   }
   265 
   266   std::set<int> comp_root;
   267   int odd_comp_num = 0;
   268   for (NodeIt n(graph); n != INVALID; ++n) {
   269     if (mm.status(n) != MaxMatching<SmartGraph>::ODD) {
   270       int root = comp.find(n);
   271       if (comp_root.find(root) == comp_root.end()) {
   272         comp_root.insert(root);
   273         if (comp.size(n) % 2 == 1) {
   274           ++odd_comp_num;
   275         }
   276       }
   277     }
   278   }
   279 
   280   check(mm.matchingSize() == num, "Wrong matching");
   281   check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
   282          "Wrong matching");
   283   return;
   284 }
   285 
   286 void checkWeightedMatching(const SmartGraph& graph,
   287                    const SmartGraph::EdgeMap<int>& weight,
   288                    const MaxWeightedMatching<SmartGraph>& mwm) {
   289   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
   290     if (graph.u(e) == graph.v(e)) continue;
   291     int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
   292 
   293     for (int i = 0; i < mwm.blossomNum(); ++i) {
   294       bool s = false, t = false;
   295       for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
   296            n != INVALID; ++n) {
   297         if (graph.u(e) == n) s = true;
   298         if (graph.v(e) == n) t = true;
   299       }
   300       if (s == true && t == true) {
   301         rw += mwm.blossomValue(i);
   302       }
   303     }
   304     rw -= weight[e] * mwm.dualScale;
   305 
   306     check(rw >= 0, "Negative reduced weight");
   307     check(rw == 0 || !mwm.matching(e),
   308           "Non-zero reduced weight on matching edge");
   309   }
   310 
   311   int pv = 0;
   312   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
   313     if (mwm.matching(n) != INVALID) {
   314       check(mwm.nodeValue(n) >= 0, "Invalid node value");
   315       pv += weight[mwm.matching(n)];
   316       SmartGraph::Node o = graph.target(mwm.matching(n));
   317       check(mwm.mate(n) == o, "Invalid matching");
   318       check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
   319             "Invalid matching");
   320     } else {
   321       check(mwm.mate(n) == INVALID, "Invalid matching");
   322       check(mwm.nodeValue(n) == 0, "Invalid matching");
   323     }
   324   }
   325 
   326   int dv = 0;
   327   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
   328     dv += mwm.nodeValue(n);
   329   }
   330 
   331   for (int i = 0; i < mwm.blossomNum(); ++i) {
   332     check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
   333     check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
   334     dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
   335   }
   336 
   337   check(pv * mwm.dualScale == dv * 2, "Wrong duality");
   338 
   339   return;
   340 }
   341 
   342 void checkWeightedPerfectMatching(const SmartGraph& graph,
   343                           const SmartGraph::EdgeMap<int>& weight,
   344                           const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
   345   for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
   346     if (graph.u(e) == graph.v(e)) continue;
   347     int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
   348 
   349     for (int i = 0; i < mwpm.blossomNum(); ++i) {
   350       bool s = false, t = false;
   351       for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
   352            n != INVALID; ++n) {
   353         if (graph.u(e) == n) s = true;
   354         if (graph.v(e) == n) t = true;
   355       }
   356       if (s == true && t == true) {
   357         rw += mwpm.blossomValue(i);
   358       }
   359     }
   360     rw -= weight[e] * mwpm.dualScale;
   361 
   362     check(rw >= 0, "Negative reduced weight");
   363     check(rw == 0 || !mwpm.matching(e),
   364           "Non-zero reduced weight on matching edge");
   365   }
   366 
   367   int pv = 0;
   368   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
   369     check(mwpm.matching(n) != INVALID, "Non perfect");
   370     pv += weight[mwpm.matching(n)];
   371     SmartGraph::Node o = graph.target(mwpm.matching(n));
   372     check(mwpm.mate(n) == o, "Invalid matching");
   373     check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
   374           "Invalid matching");
   375   }
   376 
   377   int dv = 0;
   378   for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
   379     dv += mwpm.nodeValue(n);
   380   }
   381 
   382   for (int i = 0; i < mwpm.blossomNum(); ++i) {
   383     check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
   384     check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
   385     dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
   386   }
   387 
   388   check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
   389 
   390   return;
   391 }
   392 
   393 
   394 int main() {
   395 
   396   for (int i = 0; i < lgfn; ++i) {
   397     SmartGraph graph;
   398     SmartGraph::EdgeMap<int> weight(graph);
   399 
   400     istringstream lgfs(lgf[i]);
   401     graphReader(graph, lgfs).
   402       edgeMap("weight", weight).run();
   403 
   404     MaxMatching<SmartGraph> mm(graph);
   405     mm.run();
   406     checkMatching(graph, mm);
   407 
   408     MaxWeightedMatching<SmartGraph> mwm(graph, weight);
   409     mwm.run();
   410     checkWeightedMatching(graph, weight, mwm);
   411 
   412     MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
   413     bool perfect = mwpm.run();
   414 
   415     check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
   416           "Perfect matching found");
   417 
   418     if (perfect) {
   419       checkWeightedPerfectMatching(graph, weight, mwpm);
   420     }
   421   }
   422 
   423   return 0;
   424 }