COIN-OR::LEMON - Graph Library

source: lemon-1.2/test/fractional_matching_test.cc @ 869:636dadefe1e6

Last change on this file since 869:636dadefe1e6 was 869:636dadefe1e6, checked in by Balazs Dezso <deba@…>, 10 years ago

Add fractional matching algorithms (#314)

File size: 13.0 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/fractional_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 = 4;
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  "@nodes\n"
115  "label\n"
116  "0\n"
117  "@edges\n"
118  "     label  weight\n"
119  "0 0  0      100\n"
120};
121
122void checkMaxFractionalMatchingCompile()
123{
124  typedef concepts::Graph Graph;
125  typedef Graph::Node Node;
126  typedef Graph::Edge Edge;
127
128  Graph g;
129  Node n;
130  Edge e;
131
132  MaxFractionalMatching<Graph> mat_test(g);
133  const MaxFractionalMatching<Graph>&
134    const_mat_test = mat_test;
135
136  mat_test.init();
137  mat_test.start();
138  mat_test.start(true);
139  mat_test.startPerfect();
140  mat_test.startPerfect(true);
141  mat_test.run();
142  mat_test.run(true);
143  mat_test.runPerfect();
144  mat_test.runPerfect(true);
145
146  const_mat_test.matchingSize();
147  const_mat_test.matching(e);
148  const_mat_test.matching(n);
149  const MaxFractionalMatching<Graph>::MatchingMap& mmap =
150    const_mat_test.matchingMap();
151  e = mmap[n];
152
153  const_mat_test.barrier(n);
154}
155
156void checkMaxWeightedFractionalMatchingCompile()
157{
158  typedef concepts::Graph Graph;
159  typedef Graph::Node Node;
160  typedef Graph::Edge Edge;
161  typedef Graph::EdgeMap<int> WeightMap;
162
163  Graph g;
164  Node n;
165  Edge e;
166  WeightMap w(g);
167
168  MaxWeightedFractionalMatching<Graph> mat_test(g, w);
169  const MaxWeightedFractionalMatching<Graph>&
170    const_mat_test = mat_test;
171
172  mat_test.init();
173  mat_test.start();
174  mat_test.run();
175
176  const_mat_test.matchingWeight();
177  const_mat_test.matchingSize();
178  const_mat_test.matching(e);
179  const_mat_test.matching(n);
180  const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
181    const_mat_test.matchingMap();
182  e = mmap[n];
183
184  const_mat_test.dualValue();
185  const_mat_test.nodeValue(n);
186}
187
188void checkMaxWeightedPerfectFractionalMatchingCompile()
189{
190  typedef concepts::Graph Graph;
191  typedef Graph::Node Node;
192  typedef Graph::Edge Edge;
193  typedef Graph::EdgeMap<int> WeightMap;
194
195  Graph g;
196  Node n;
197  Edge e;
198  WeightMap w(g);
199
200  MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
201  const MaxWeightedPerfectFractionalMatching<Graph>&
202    const_mat_test = mat_test;
203
204  mat_test.init();
205  mat_test.start();
206  mat_test.run();
207
208  const_mat_test.matchingWeight();
209  const_mat_test.matching(e);
210  const_mat_test.matching(n);
211  const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
212    const_mat_test.matchingMap();
213  e = mmap[n];
214
215  const_mat_test.dualValue();
216  const_mat_test.nodeValue(n);
217}
218
219void checkFractionalMatching(const SmartGraph& graph,
220                             const MaxFractionalMatching<SmartGraph>& mfm,
221                             bool allow_loops = true) {
222  int pv = 0;
223  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
224    int indeg = 0;
225    for (InArcIt a(graph, n); a != INVALID; ++a) {
226      if (mfm.matching(graph.source(a)) == a) {
227        ++indeg;
228      }
229    }
230    if (mfm.matching(n) != INVALID) {
231      check(indeg == 1, "Invalid matching");
232      ++pv;
233    } else {
234      check(indeg == 0, "Invalid matching");
235    }
236  }
237  check(pv == mfm.matchingSize(), "Wrong matching size");
238
239  SmartGraph::NodeMap<bool> processed(graph, false);
240  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
241    if (processed[n]) continue;
242    processed[n] = true;
243    if (mfm.matching(n) == INVALID) continue;
244    int num = 1;
245    Node v = graph.target(mfm.matching(n));
246    while (v != n) {
247      processed[v] = true;
248      ++num;
249      v = graph.target(mfm.matching(v));
250    }
251    check(num == 2 || num % 2 == 1, "Wrong cycle size");
252    check(allow_loops || num != 1, "Wrong cycle size");
253  }
254
255  int anum = 0, bnum = 0;
256  SmartGraph::NodeMap<bool> neighbours(graph, false);
257  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
258    if (!mfm.barrier(n)) continue;
259    ++anum;
260    for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
261      Node u = graph.source(a);
262      if (!allow_loops && u == n) continue;
263      if (!neighbours[u]) {
264        neighbours[u] = true;
265        ++bnum;
266      }
267    }
268  }
269  check(anum - bnum + mfm.matchingSize() == countNodes(graph),
270        "Wrong barrier");
271}
272
273void checkPerfectFractionalMatching(const SmartGraph& graph,
274                             const MaxFractionalMatching<SmartGraph>& mfm,
275                             bool perfect, bool allow_loops = true) {
276  if (perfect) {
277    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
278      int indeg = 0;
279      for (InArcIt a(graph, n); a != INVALID; ++a) {
280        if (mfm.matching(graph.source(a)) == a) {
281          ++indeg;
282        }
283      }
284      check(mfm.matching(n) != INVALID, "Invalid matching");
285      check(indeg == 1, "Invalid matching");
286    }
287  } else {
288    int anum = 0, bnum = 0;
289    SmartGraph::NodeMap<bool> neighbours(graph, false);
290    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
291      if (!mfm.barrier(n)) continue;
292      ++anum;
293      for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
294        Node u = graph.source(a);
295        if (!allow_loops && u == n) continue;
296        if (!neighbours[u]) {
297          neighbours[u] = true;
298          ++bnum;
299        }
300      }
301    }
302    check(anum - bnum > 0, "Wrong barrier");
303  }
304}
305
306void checkWeightedFractionalMatching(const SmartGraph& graph,
307                   const SmartGraph::EdgeMap<int>& weight,
308                   const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
309                   bool allow_loops = true) {
310  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
311    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
312    int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
313      - weight[e] * mwfm.dualScale;
314
315    check(rw >= 0, "Negative reduced weight");
316    check(rw == 0 || !mwfm.matching(e),
317          "Non-zero reduced weight on matching edge");
318  }
319
320  int pv = 0;
321  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
322    int indeg = 0;
323    for (InArcIt a(graph, n); a != INVALID; ++a) {
324      if (mwfm.matching(graph.source(a)) == a) {
325        ++indeg;
326      }
327    }
328    check(indeg <= 1, "Invalid matching");
329    if (mwfm.matching(n) != INVALID) {
330      check(mwfm.nodeValue(n) >= 0, "Invalid node value");
331      check(indeg == 1, "Invalid matching");
332      pv += weight[mwfm.matching(n)];
333      SmartGraph::Node o = graph.target(mwfm.matching(n));
334    } else {
335      check(mwfm.nodeValue(n) == 0, "Invalid matching");
336      check(indeg == 0, "Invalid matching");
337    }
338  }
339
340  int dv = 0;
341  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
342    dv += mwfm.nodeValue(n);
343  }
344
345  check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
346
347  SmartGraph::NodeMap<bool> processed(graph, false);
348  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
349    if (processed[n]) continue;
350    processed[n] = true;
351    if (mwfm.matching(n) == INVALID) continue;
352    int num = 1;
353    Node v = graph.target(mwfm.matching(n));
354    while (v != n) {
355      processed[v] = true;
356      ++num;
357      v = graph.target(mwfm.matching(v));
358    }
359    check(num == 2 || num % 2 == 1, "Wrong cycle size");
360    check(allow_loops || num != 1, "Wrong cycle size");
361  }
362
363  return;
364}
365
366void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
367                const SmartGraph::EdgeMap<int>& weight,
368                const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
369                bool allow_loops = true) {
370  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
371    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
372    int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
373      - weight[e] * mwpfm.dualScale;
374
375    check(rw >= 0, "Negative reduced weight");
376    check(rw == 0 || !mwpfm.matching(e),
377          "Non-zero reduced weight on matching edge");
378  }
379
380  int pv = 0;
381  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
382    int indeg = 0;
383    for (InArcIt a(graph, n); a != INVALID; ++a) {
384      if (mwpfm.matching(graph.source(a)) == a) {
385        ++indeg;
386      }
387    }
388    check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
389    check(indeg == 1, "Invalid perfect matching");
390    pv += weight[mwpfm.matching(n)];
391    SmartGraph::Node o = graph.target(mwpfm.matching(n));
392  }
393
394  int dv = 0;
395  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
396    dv += mwpfm.nodeValue(n);
397  }
398
399  check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
400
401  SmartGraph::NodeMap<bool> processed(graph, false);
402  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
403    if (processed[n]) continue;
404    processed[n] = true;
405    if (mwpfm.matching(n) == INVALID) continue;
406    int num = 1;
407    Node v = graph.target(mwpfm.matching(n));
408    while (v != n) {
409      processed[v] = true;
410      ++num;
411      v = graph.target(mwpfm.matching(v));
412    }
413    check(num == 2 || num % 2 == 1, "Wrong cycle size");
414    check(allow_loops || num != 1, "Wrong cycle size");
415  }
416
417  return;
418}
419
420
421int main() {
422
423  for (int i = 0; i < lgfn; ++i) {
424    SmartGraph graph;
425    SmartGraph::EdgeMap<int> weight(graph);
426
427    istringstream lgfs(lgf[i]);
428    graphReader(graph, lgfs).
429      edgeMap("weight", weight).run();
430
431    bool perfect_with_loops;
432    {
433      MaxFractionalMatching<SmartGraph> mfm(graph, true);
434      mfm.run();
435      checkFractionalMatching(graph, mfm, true);
436      perfect_with_loops = mfm.matchingSize() == countNodes(graph);
437    }
438
439    bool perfect_without_loops;
440    {
441      MaxFractionalMatching<SmartGraph> mfm(graph, false);
442      mfm.run();
443      checkFractionalMatching(graph, mfm, false);
444      perfect_without_loops = mfm.matchingSize() == countNodes(graph);
445    }
446
447    {
448      MaxFractionalMatching<SmartGraph> mfm(graph, true);
449      bool result = mfm.runPerfect();
450      checkPerfectFractionalMatching(graph, mfm, result, true);
451      check(result == perfect_with_loops, "Wrong perfect matching");
452    }
453
454    {
455      MaxFractionalMatching<SmartGraph> mfm(graph, false);
456      bool result = mfm.runPerfect();
457      checkPerfectFractionalMatching(graph, mfm, result, false);
458      check(result == perfect_without_loops, "Wrong perfect matching");
459    }
460
461    {
462      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
463      mwfm.run();
464      checkWeightedFractionalMatching(graph, weight, mwfm, true);
465    }
466
467    {
468      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
469      mwfm.run();
470      checkWeightedFractionalMatching(graph, weight, mwfm, false);
471    }
472
473    {
474      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
475                                                             true);
476      bool perfect = mwpfm.run();
477      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
478            "Perfect matching found");
479      check(perfect == perfect_with_loops, "Wrong perfect matching");
480
481      if (perfect) {
482        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
483      }
484    }
485
486    {
487      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
488                                                             false);
489      bool perfect = mwpfm.run();
490      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
491            "Perfect matching found");
492      check(perfect == perfect_without_loops, "Wrong perfect matching");
493
494      if (perfect) {
495        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
496      }
497    }
498
499  }
500
501  return 0;
502}
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