test/max_matching_test.cc
author Balazs Dezso <deba@inf.elte.hu>
Sun, 30 Nov 2008 18:57:18 +0100
changeset 414 05357da973ce
parent 326 64ad48007fb2
child 440 88ed40ad0d4f
permissions -rw-r--r--
Port graph adaptors from svn -r3498 (#67)
deba@326
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@326
     2
 *
deba@326
     3
 * This file is a part of LEMON, a generic C++ optimization library.
deba@326
     4
 *
deba@326
     5
 * Copyright (C) 2003-2008
deba@326
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@326
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@326
     8
 *
deba@326
     9
 * Permission to use, modify and distribute this software is granted
deba@326
    10
 * provided that this copyright notice appears in all copies. For
deba@326
    11
 * precise terms see the accompanying LICENSE file.
deba@326
    12
 *
deba@326
    13
 * This software is provided "AS IS" with no warranty of any kind,
deba@326
    14
 * express or implied, and with no claim as to its suitability for any
deba@326
    15
 * purpose.
deba@326
    16
 *
deba@326
    17
 */
deba@326
    18
deba@326
    19
#include <iostream>
deba@327
    20
#include <sstream>
deba@326
    21
#include <vector>
deba@326
    22
#include <queue>
deba@326
    23
#include <lemon/math.h>
deba@326
    24
#include <cstdlib>
deba@326
    25
deba@327
    26
#include <lemon/max_matching.h>
deba@327
    27
#include <lemon/smart_graph.h>
deba@327
    28
#include <lemon/lgf_reader.h>
deba@327
    29
deba@326
    30
#include "test_tools.h"
deba@326
    31
deba@326
    32
using namespace std;
deba@326
    33
using namespace lemon;
deba@326
    34
deba@327
    35
GRAPH_TYPEDEFS(SmartGraph);
deba@327
    36
deba@327
    37
deba@327
    38
const int lgfn = 3;
deba@327
    39
const std::string lgf[lgfn] = {
deba@327
    40
  "@nodes\n"
deba@327
    41
  "label\n"
deba@327
    42
  "0\n"
deba@327
    43
  "1\n"
deba@327
    44
  "2\n"
deba@327
    45
  "3\n"
deba@327
    46
  "4\n"
deba@327
    47
  "5\n"
deba@327
    48
  "6\n"
deba@327
    49
  "7\n"
deba@327
    50
  "@edges\n"
deba@327
    51
  "     label  weight\n"
deba@327
    52
  "7 4  0      984\n"
deba@327
    53
  "0 7  1      73\n"
deba@327
    54
  "7 1  2      204\n"
deba@327
    55
  "2 3  3      583\n"
deba@327
    56
  "2 7  4      565\n"
deba@327
    57
  "2 1  5      582\n"
deba@327
    58
  "0 4  6      551\n"
deba@327
    59
  "2 5  7      385\n"
deba@327
    60
  "1 5  8      561\n"
deba@327
    61
  "5 3  9      484\n"
deba@327
    62
  "7 5  10     904\n"
deba@327
    63
  "3 6  11     47\n"
deba@327
    64
  "7 6  12     888\n"
deba@327
    65
  "3 0  13     747\n"
deba@327
    66
  "6 1  14     310\n",
deba@327
    67
deba@327
    68
  "@nodes\n"
deba@327
    69
  "label\n"
deba@327
    70
  "0\n"
deba@327
    71
  "1\n"
deba@327
    72
  "2\n"
deba@327
    73
  "3\n"
deba@327
    74
  "4\n"
deba@327
    75
  "5\n"
deba@327
    76
  "6\n"
deba@327
    77
  "7\n"
deba@327
    78
  "@edges\n"
deba@327
    79
  "     label  weight\n"
deba@327
    80
  "2 5  0      710\n"
deba@327
    81
  "0 5  1      241\n"
deba@327
    82
  "2 4  2      856\n"
deba@327
    83
  "2 6  3      762\n"
deba@327
    84
  "4 1  4      747\n"
deba@327
    85
  "6 1  5      962\n"
deba@327
    86
  "4 7  6      723\n"
deba@327
    87
  "1 7  7      661\n"
deba@327
    88
  "2 3  8      376\n"
deba@327
    89
  "1 0  9      416\n"
deba@327
    90
  "6 7  10     391\n",
deba@327
    91
deba@327
    92
  "@nodes\n"
deba@327
    93
  "label\n"
deba@327
    94
  "0\n"
deba@327
    95
  "1\n"
deba@327
    96
  "2\n"
deba@327
    97
  "3\n"
deba@327
    98
  "4\n"
deba@327
    99
  "5\n"
deba@327
   100
  "6\n"
deba@327
   101
  "7\n"
deba@327
   102
  "@edges\n"
deba@327
   103
  "     label  weight\n"
deba@327
   104
  "6 2  0      553\n"
deba@327
   105
  "0 7  1      653\n"
deba@327
   106
  "6 3  2      22\n"
deba@327
   107
  "4 7  3      846\n"
deba@327
   108
  "7 2  4      981\n"
deba@327
   109
  "7 6  5      250\n"
deba@327
   110
  "5 2  6      539\n",
deba@327
   111
};
deba@327
   112
deba@327
   113
void checkMatching(const SmartGraph& graph,
deba@327
   114
                   const MaxMatching<SmartGraph>& mm) {
deba@327
   115
  int num = 0;
deba@327
   116
deba@327
   117
  IntNodeMap comp_index(graph);
deba@327
   118
  UnionFind<IntNodeMap> comp(comp_index);
deba@327
   119
deba@327
   120
  int barrier_num = 0;
deba@327
   121
deba@327
   122
  for (NodeIt n(graph); n != INVALID; ++n) {
deba@327
   123
    check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
deba@327
   124
          mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
deba@327
   125
    if (mm.decomposition(n) == MaxMatching<SmartGraph>::ODD) {
deba@327
   126
      ++barrier_num;
deba@327
   127
    } else {
deba@327
   128
      comp.insert(n);
deba@327
   129
    }
deba@327
   130
  }
deba@327
   131
deba@327
   132
  for (EdgeIt e(graph); e != INVALID; ++e) {
deba@327
   133
    if (mm.matching(e)) {
deba@327
   134
      check(e == mm.matching(graph.u(e)), "Wrong matching");
deba@327
   135
      check(e == mm.matching(graph.v(e)), "Wrong matching");
deba@327
   136
      ++num;
deba@327
   137
    }
deba@327
   138
    check(mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
deba@327
   139
          mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
deba@327
   140
          "Wrong Gallai-Edmonds decomposition");
deba@327
   141
deba@327
   142
    check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
deba@327
   143
          mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
deba@327
   144
          "Wrong Gallai-Edmonds decomposition");
deba@327
   145
deba@327
   146
    if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
deba@327
   147
        mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
deba@327
   148
      comp.join(graph.u(e), graph.v(e));
deba@327
   149
    }
deba@327
   150
  }
deba@327
   151
deba@327
   152
  std::set<int> comp_root;
deba@327
   153
  int odd_comp_num = 0;
deba@327
   154
  for (NodeIt n(graph); n != INVALID; ++n) {
deba@327
   155
    if (mm.decomposition(n) != MaxMatching<SmartGraph>::ODD) {
deba@327
   156
      int root = comp.find(n);
deba@327
   157
      if (comp_root.find(root) == comp_root.end()) {
deba@327
   158
        comp_root.insert(root);
deba@327
   159
        if (comp.size(n) % 2 == 1) {
deba@327
   160
          ++odd_comp_num;
deba@327
   161
        }
deba@327
   162
      }
deba@327
   163
    }
deba@327
   164
  }
deba@327
   165
deba@327
   166
  check(mm.matchingSize() == num, "Wrong matching");
deba@327
   167
  check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
deba@327
   168
         "Wrong matching");
deba@327
   169
  return;
deba@327
   170
}
deba@327
   171
deba@327
   172
void checkWeightedMatching(const SmartGraph& graph,
deba@327
   173
                   const SmartGraph::EdgeMap<int>& weight,
deba@327
   174
                   const MaxWeightedMatching<SmartGraph>& mwm) {
deba@327
   175
  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@327
   176
    if (graph.u(e) == graph.v(e)) continue;
deba@327
   177
    int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
deba@327
   178
deba@327
   179
    for (int i = 0; i < mwm.blossomNum(); ++i) {
deba@327
   180
      bool s = false, t = false;
deba@327
   181
      for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
deba@327
   182
           n != INVALID; ++n) {
deba@327
   183
        if (graph.u(e) == n) s = true;
deba@327
   184
        if (graph.v(e) == n) t = true;
deba@327
   185
      }
deba@327
   186
      if (s == true && t == true) {
deba@327
   187
        rw += mwm.blossomValue(i);
deba@327
   188
      }
deba@327
   189
    }
deba@327
   190
    rw -= weight[e] * mwm.dualScale;
deba@327
   191
deba@327
   192
    check(rw >= 0, "Negative reduced weight");
deba@327
   193
    check(rw == 0 || !mwm.matching(e),
deba@327
   194
          "Non-zero reduced weight on matching edge");
deba@327
   195
  }
deba@327
   196
deba@327
   197
  int pv = 0;
deba@327
   198
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@327
   199
    if (mwm.matching(n) != INVALID) {
deba@327
   200
      check(mwm.nodeValue(n) >= 0, "Invalid node value");
deba@327
   201
      pv += weight[mwm.matching(n)];
deba@327
   202
      SmartGraph::Node o = graph.target(mwm.matching(n));
deba@327
   203
      check(mwm.mate(n) == o, "Invalid matching");
deba@327
   204
      check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
deba@327
   205
            "Invalid matching");
deba@327
   206
    } else {
deba@327
   207
      check(mwm.mate(n) == INVALID, "Invalid matching");
deba@327
   208
      check(mwm.nodeValue(n) == 0, "Invalid matching");
deba@327
   209
    }
deba@327
   210
  }
deba@327
   211
deba@327
   212
  int dv = 0;
deba@327
   213
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@327
   214
    dv += mwm.nodeValue(n);
deba@327
   215
  }
deba@327
   216
deba@327
   217
  for (int i = 0; i < mwm.blossomNum(); ++i) {
deba@327
   218
    check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
deba@327
   219
    check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
deba@327
   220
    dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
deba@327
   221
  }
deba@327
   222
deba@327
   223
  check(pv * mwm.dualScale == dv * 2, "Wrong duality");
deba@327
   224
deba@327
   225
  return;
deba@327
   226
}
deba@327
   227
deba@327
   228
void checkWeightedPerfectMatching(const SmartGraph& graph,
deba@327
   229
                          const SmartGraph::EdgeMap<int>& weight,
deba@327
   230
                          const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
deba@327
   231
  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@327
   232
    if (graph.u(e) == graph.v(e)) continue;
deba@327
   233
    int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
deba@327
   234
deba@327
   235
    for (int i = 0; i < mwpm.blossomNum(); ++i) {
deba@327
   236
      bool s = false, t = false;
deba@327
   237
      for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
deba@327
   238
           n != INVALID; ++n) {
deba@327
   239
        if (graph.u(e) == n) s = true;
deba@327
   240
        if (graph.v(e) == n) t = true;
deba@327
   241
      }
deba@327
   242
      if (s == true && t == true) {
deba@327
   243
        rw += mwpm.blossomValue(i);
deba@327
   244
      }
deba@327
   245
    }
deba@327
   246
    rw -= weight[e] * mwpm.dualScale;
deba@327
   247
deba@327
   248
    check(rw >= 0, "Negative reduced weight");
deba@327
   249
    check(rw == 0 || !mwpm.matching(e),
deba@327
   250
          "Non-zero reduced weight on matching edge");
deba@327
   251
  }
deba@327
   252
deba@327
   253
  int pv = 0;
deba@327
   254
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@327
   255
    check(mwpm.matching(n) != INVALID, "Non perfect");
deba@327
   256
    pv += weight[mwpm.matching(n)];
deba@327
   257
    SmartGraph::Node o = graph.target(mwpm.matching(n));
deba@327
   258
    check(mwpm.mate(n) == o, "Invalid matching");
deba@327
   259
    check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
deba@327
   260
          "Invalid matching");
deba@327
   261
  }
deba@327
   262
deba@327
   263
  int dv = 0;
deba@327
   264
  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@327
   265
    dv += mwpm.nodeValue(n);
deba@327
   266
  }
deba@327
   267
deba@327
   268
  for (int i = 0; i < mwpm.blossomNum(); ++i) {
deba@327
   269
    check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
deba@327
   270
    check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
deba@327
   271
    dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
deba@327
   272
  }
deba@327
   273
deba@327
   274
  check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
deba@327
   275
deba@327
   276
  return;
deba@327
   277
}
deba@327
   278
deba@327
   279
deba@326
   280
int main() {
deba@326
   281
deba@327
   282
  for (int i = 0; i < lgfn; ++i) {
deba@327
   283
    SmartGraph graph;
deba@327
   284
    SmartGraph::EdgeMap<int> weight(graph);
deba@326
   285
deba@327
   286
    istringstream lgfs(lgf[i]);
deba@327
   287
    graphReader(graph, lgfs).
deba@327
   288
      edgeMap("weight", weight).run();
deba@326
   289
deba@327
   290
    MaxMatching<SmartGraph> mm(graph);
deba@327
   291
    mm.run();
deba@327
   292
    checkMatching(graph, mm);
deba@326
   293
deba@327
   294
    MaxWeightedMatching<SmartGraph> mwm(graph, weight);
deba@327
   295
    mwm.run();
deba@327
   296
    checkWeightedMatching(graph, weight, mwm);
deba@326
   297
deba@327
   298
    MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
deba@327
   299
    bool perfect = mwpm.run();
deba@326
   300
deba@327
   301
    check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
deba@327
   302
          "Perfect matching found");
deba@326
   303
deba@327
   304
    if (perfect) {
deba@327
   305
      checkWeightedPerfectMatching(graph, weight, mwpm);
deba@326
   306
    }
deba@326
   307
  }
deba@326
   308
deba@326
   309
  return 0;
deba@326
   310
}