test/max_matching_test.cc
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 20 Feb 2009 21:37:19 +0000
changeset 517 2b6d5d22bb23
parent 327 91d63b8b1a4c
child 590 b61354458b59
permissions -rw-r--r--
Merge
     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 <lemon/math.h>
    24 #include <cstdlib>
    25 
    26 #include <lemon/max_matching.h>
    27 #include <lemon/smart_graph.h>
    28 #include <lemon/lgf_reader.h>
    29 
    30 #include "test_tools.h"
    31 
    32 using namespace std;
    33 using namespace lemon;
    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 
   280 int main() {
   281 
   282   for (int i = 0; i < lgfn; ++i) {
   283     SmartGraph graph;
   284     SmartGraph::EdgeMap<int> weight(graph);
   285 
   286     istringstream lgfs(lgf[i]);
   287     graphReader(graph, lgfs).
   288       edgeMap("weight", weight).run();
   289 
   290     MaxMatching<SmartGraph> mm(graph);
   291     mm.run();
   292     checkMatching(graph, mm);
   293 
   294     MaxWeightedMatching<SmartGraph> mwm(graph, weight);
   295     mwm.run();
   296     checkWeightedMatching(graph, weight, mwm);
   297 
   298     MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
   299     bool perfect = mwpm.run();
   300 
   301     check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
   302           "Perfect matching found");
   303 
   304     if (perfect) {
   305       checkWeightedPerfectMatching(graph, weight, mwpm);
   306     }
   307   }
   308 
   309   return 0;
   310 }