COIN-OR::LEMON - Graph Library

source: lemon/test/matching_test.cc @ 1392:7c86f14b3bc5

Last change on this file since 1392:7c86f14b3bc5 was 1270:dceba191c00d, checked in by Alpar Juttner <alpar@…>, 6 years ago

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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) 2003-2013
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  ::lemon::ignore_unused_variable_warning(stat);
149  const MaxMatching<Graph>::StatusMap& smap =
150    const_mat_test.statusMap();
151  stat = smap[n];
152  const_mat_test.barrier(n);
153}
154
155void checkMaxWeightedMatchingCompile()
156{
157  typedef concepts::Graph Graph;
158  typedef Graph::Node Node;
159  typedef Graph::Edge Edge;
160  typedef Graph::EdgeMap<int> WeightMap;
161
162  Graph g;
163  Node n;
164  Edge e;
165  WeightMap w(g);
166
167  MaxWeightedMatching<Graph> mat_test(g, w);
168  const MaxWeightedMatching<Graph>&
169    const_mat_test = mat_test;
170
171  mat_test.init();
172  mat_test.start();
173  mat_test.run();
174
175  const_mat_test.matchingWeight();
176  const_mat_test.matchingSize();
177  const_mat_test.matching(e);
178  const_mat_test.matching(n);
179  const MaxWeightedMatching<Graph>::MatchingMap& mmap =
180    const_mat_test.matchingMap();
181  e = mmap[n];
182  const_mat_test.mate(n);
183
184  int k = 0;
185  const_mat_test.dualValue();
186  const_mat_test.nodeValue(n);
187  const_mat_test.blossomNum();
188  const_mat_test.blossomSize(k);
189  const_mat_test.blossomValue(k);
190}
191
192void checkMaxWeightedPerfectMatchingCompile()
193{
194  typedef concepts::Graph Graph;
195  typedef Graph::Node Node;
196  typedef Graph::Edge Edge;
197  typedef Graph::EdgeMap<int> WeightMap;
198
199  Graph g;
200  Node n;
201  Edge e;
202  WeightMap w(g);
203
204  MaxWeightedPerfectMatching<Graph> mat_test(g, w);
205  const MaxWeightedPerfectMatching<Graph>&
206    const_mat_test = mat_test;
207
208  mat_test.init();
209  mat_test.start();
210  mat_test.run();
211
212  const_mat_test.matchingWeight();
213  const_mat_test.matching(e);
214  const_mat_test.matching(n);
215  const MaxWeightedPerfectMatching<Graph>::MatchingMap& mmap =
216    const_mat_test.matchingMap();
217  e = mmap[n];
218  const_mat_test.mate(n);
219
220  int k = 0;
221  const_mat_test.dualValue();
222  const_mat_test.nodeValue(n);
223  const_mat_test.blossomNum();
224  const_mat_test.blossomSize(k);
225  const_mat_test.blossomValue(k);
226}
227
228void checkMatching(const SmartGraph& graph,
229                   const MaxMatching<SmartGraph>& mm) {
230  int num = 0;
231
232  IntNodeMap comp_index(graph);
233  UnionFind<IntNodeMap> comp(comp_index);
234
235  int barrier_num = 0;
236
237  for (NodeIt n(graph); n != INVALID; ++n) {
238    check(mm.status(n) == MaxMatching<SmartGraph>::EVEN ||
239          mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
240    if (mm.status(n) == MaxMatching<SmartGraph>::ODD) {
241      ++barrier_num;
242    } else {
243      comp.insert(n);
244    }
245  }
246
247  for (EdgeIt e(graph); e != INVALID; ++e) {
248    if (mm.matching(e)) {
249      check(e == mm.matching(graph.u(e)), "Wrong matching");
250      check(e == mm.matching(graph.v(e)), "Wrong matching");
251      ++num;
252    }
253    check(mm.status(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
254          mm.status(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
255          "Wrong Gallai-Edmonds decomposition");
256
257    check(mm.status(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
258          mm.status(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
259          "Wrong Gallai-Edmonds decomposition");
260
261    if (mm.status(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
262        mm.status(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
263      comp.join(graph.u(e), graph.v(e));
264    }
265  }
266
267  std::set<int> comp_root;
268  int odd_comp_num = 0;
269  for (NodeIt n(graph); n != INVALID; ++n) {
270    if (mm.status(n) != MaxMatching<SmartGraph>::ODD) {
271      int root = comp.find(n);
272      if (comp_root.find(root) == comp_root.end()) {
273        comp_root.insert(root);
274        if (comp.size(n) % 2 == 1) {
275          ++odd_comp_num;
276        }
277      }
278    }
279  }
280
281  check(mm.matchingSize() == num, "Wrong matching");
282  check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
283         "Wrong matching");
284  return;
285}
286
287void checkWeightedMatching(const SmartGraph& graph,
288                   const SmartGraph::EdgeMap<int>& weight,
289                   const MaxWeightedMatching<SmartGraph>& mwm) {
290  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
291    if (graph.u(e) == graph.v(e)) continue;
292    int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
293
294    for (int i = 0; i < mwm.blossomNum(); ++i) {
295      bool s = false, t = false;
296      for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
297           n != INVALID; ++n) {
298        if (graph.u(e) == n) s = true;
299        if (graph.v(e) == n) t = true;
300      }
301      if (s == true && t == true) {
302        rw += mwm.blossomValue(i);
303      }
304    }
305    rw -= weight[e] * mwm.dualScale;
306
307    check(rw >= 0, "Negative reduced weight");
308    check(rw == 0 || !mwm.matching(e),
309          "Non-zero reduced weight on matching edge");
310  }
311
312  int pv = 0;
313  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
314    if (mwm.matching(n) != INVALID) {
315      check(mwm.nodeValue(n) >= 0, "Invalid node value");
316      pv += weight[mwm.matching(n)];
317      SmartGraph::Node o = graph.target(mwm.matching(n));
318      check(mwm.mate(n) == o, "Invalid matching");
319      check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
320            "Invalid matching");
321    } else {
322      check(mwm.mate(n) == INVALID, "Invalid matching");
323      check(mwm.nodeValue(n) == 0, "Invalid matching");
324    }
325  }
326
327  int dv = 0;
328  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
329    dv += mwm.nodeValue(n);
330  }
331
332  for (int i = 0; i < mwm.blossomNum(); ++i) {
333    check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
334    check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
335    dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
336  }
337
338  check(pv * mwm.dualScale == dv * 2, "Wrong duality");
339
340  return;
341}
342
343void checkWeightedPerfectMatching(const SmartGraph& graph,
344                          const SmartGraph::EdgeMap<int>& weight,
345                          const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
346  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
347    if (graph.u(e) == graph.v(e)) continue;
348    int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
349
350    for (int i = 0; i < mwpm.blossomNum(); ++i) {
351      bool s = false, t = false;
352      for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
353           n != INVALID; ++n) {
354        if (graph.u(e) == n) s = true;
355        if (graph.v(e) == n) t = true;
356      }
357      if (s == true && t == true) {
358        rw += mwpm.blossomValue(i);
359      }
360    }
361    rw -= weight[e] * mwpm.dualScale;
362
363    check(rw >= 0, "Negative reduced weight");
364    check(rw == 0 || !mwpm.matching(e),
365          "Non-zero reduced weight on matching edge");
366  }
367
368  int pv = 0;
369  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
370    check(mwpm.matching(n) != INVALID, "Non perfect");
371    pv += weight[mwpm.matching(n)];
372    SmartGraph::Node o = graph.target(mwpm.matching(n));
373    check(mwpm.mate(n) == o, "Invalid matching");
374    check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
375          "Invalid matching");
376  }
377
378  int dv = 0;
379  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
380    dv += mwpm.nodeValue(n);
381  }
382
383  for (int i = 0; i < mwpm.blossomNum(); ++i) {
384    check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
385    check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
386    dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
387  }
388
389  check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
390
391  return;
392}
393
394
395int main() {
396
397  for (int i = 0; i < lgfn; ++i) {
398    SmartGraph graph;
399    SmartGraph::EdgeMap<int> weight(graph);
400
401    istringstream lgfs(lgf[i]);
402    graphReader(graph, lgfs).
403      edgeMap("weight", weight).run();
404
405    bool perfect;
406    {
407      MaxMatching<SmartGraph> mm(graph);
408      mm.run();
409      checkMatching(graph, mm);
410      perfect = 2 * mm.matchingSize() == countNodes(graph);
411    }
412
413    {
414      MaxWeightedMatching<SmartGraph> mwm(graph, weight);
415      mwm.run();
416      checkWeightedMatching(graph, weight, mwm);
417    }
418
419    {
420      MaxWeightedMatching<SmartGraph> mwm(graph, weight);
421      mwm.init();
422      mwm.start();
423      checkWeightedMatching(graph, weight, mwm);
424    }
425
426    {
427      MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
428      bool result = mwpm.run();
429
430      check(result == perfect, "Perfect matching found");
431      if (perfect) {
432        checkWeightedPerfectMatching(graph, weight, mwpm);
433      }
434    }
435
436    {
437      MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
438      mwpm.init();
439      bool result = mwpm.start();
440
441      check(result == perfect, "Perfect matching found");
442      if (perfect) {
443        checkWeightedPerfectMatching(graph, weight, mwpm);
444      }
445    }
446  }
447
448  return 0;
449}
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