COIN-OR::LEMON - Graph Library

source: lemon/test/matching_test.cc @ 641:d657c71db7db

Last change on this file since 641:d657c71db7db was 641:d657c71db7db, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Rename max_matching.h to matching.h (#265)

File size: 10.5 KB
Line 
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
34using namespace std;
35using namespace lemon;
36
37GRAPH_TYPEDEFS(SmartGraph);
38
39
40const int lgfn = 3;
41const 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
115void 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
154void 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
191void 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
227void 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
286void 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
342void 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
394int 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}
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