COIN-OR::LEMON - Graph Library

source: lemon-1.2/test/fractional_matching_test.cc @ 877:141f9c0db4a3

Last change on this file since 877:141f9c0db4a3 was 877:141f9c0db4a3, checked in by Alpar Juttner <alpar@…>, 10 years ago

Unify the sources (#339)

File size: 13.9 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) 2003-2010
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  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
240    check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
241          (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
242          mfm.matching(e), "Invalid matching");
243  }
244
245  SmartGraph::NodeMap<bool> processed(graph, false);
246  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
247    if (processed[n]) continue;
248    processed[n] = true;
249    if (mfm.matching(n) == INVALID) continue;
250    int num = 1;
251    Node v = graph.target(mfm.matching(n));
252    while (v != n) {
253      processed[v] = true;
254      ++num;
255      v = graph.target(mfm.matching(v));
256    }
257    check(num == 2 || num % 2 == 1, "Wrong cycle size");
258    check(allow_loops || num != 1, "Wrong cycle size");
259  }
260
261  int anum = 0, bnum = 0;
262  SmartGraph::NodeMap<bool> neighbours(graph, false);
263  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
264    if (!mfm.barrier(n)) continue;
265    ++anum;
266    for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
267      Node u = graph.source(a);
268      if (!allow_loops && u == n) continue;
269      if (!neighbours[u]) {
270        neighbours[u] = true;
271        ++bnum;
272      }
273    }
274  }
275  check(anum - bnum + mfm.matchingSize() == countNodes(graph),
276        "Wrong barrier");
277}
278
279void checkPerfectFractionalMatching(const SmartGraph& graph,
280                             const MaxFractionalMatching<SmartGraph>& mfm,
281                             bool perfect, bool allow_loops = true) {
282  if (perfect) {
283    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
284      int indeg = 0;
285      for (InArcIt a(graph, n); a != INVALID; ++a) {
286        if (mfm.matching(graph.source(a)) == a) {
287          ++indeg;
288        }
289      }
290      check(mfm.matching(n) != INVALID, "Invalid matching");
291      check(indeg == 1, "Invalid matching");
292    }
293    for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
294      check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
295            (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
296            mfm.matching(e), "Invalid matching");
297    }
298  } else {
299    int anum = 0, bnum = 0;
300    SmartGraph::NodeMap<bool> neighbours(graph, false);
301    for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
302      if (!mfm.barrier(n)) continue;
303      ++anum;
304      for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
305        Node u = graph.source(a);
306        if (!allow_loops && u == n) continue;
307        if (!neighbours[u]) {
308          neighbours[u] = true;
309          ++bnum;
310        }
311      }
312    }
313    check(anum - bnum > 0, "Wrong barrier");
314  }
315}
316
317void checkWeightedFractionalMatching(const SmartGraph& graph,
318                   const SmartGraph::EdgeMap<int>& weight,
319                   const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
320                   bool allow_loops = true) {
321  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
322    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
323    int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
324      - weight[e] * mwfm.dualScale;
325
326    check(rw >= 0, "Negative reduced weight");
327    check(rw == 0 || !mwfm.matching(e),
328          "Non-zero reduced weight on matching edge");
329  }
330
331  int pv = 0;
332  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
333    int indeg = 0;
334    for (InArcIt a(graph, n); a != INVALID; ++a) {
335      if (mwfm.matching(graph.source(a)) == a) {
336        ++indeg;
337      }
338    }
339    check(indeg <= 1, "Invalid matching");
340    if (mwfm.matching(n) != INVALID) {
341      check(mwfm.nodeValue(n) >= 0, "Invalid node value");
342      check(indeg == 1, "Invalid matching");
343      pv += weight[mwfm.matching(n)];
344      SmartGraph::Node o = graph.target(mwfm.matching(n));
345    } else {
346      check(mwfm.nodeValue(n) == 0, "Invalid matching");
347      check(indeg == 0, "Invalid matching");
348    }
349  }
350
351  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
352    check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +
353          (e == mwfm.matching(graph.v(e)) ? 1 : 0) ==
354          mwfm.matching(e), "Invalid matching");
355  }
356
357  int dv = 0;
358  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
359    dv += mwfm.nodeValue(n);
360  }
361
362  check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
363
364  SmartGraph::NodeMap<bool> processed(graph, false);
365  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
366    if (processed[n]) continue;
367    processed[n] = true;
368    if (mwfm.matching(n) == INVALID) continue;
369    int num = 1;
370    Node v = graph.target(mwfm.matching(n));
371    while (v != n) {
372      processed[v] = true;
373      ++num;
374      v = graph.target(mwfm.matching(v));
375    }
376    check(num == 2 || num % 2 == 1, "Wrong cycle size");
377    check(allow_loops || num != 1, "Wrong cycle size");
378  }
379
380  return;
381}
382
383void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
384                const SmartGraph::EdgeMap<int>& weight,
385                const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
386                bool allow_loops = true) {
387  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
388    if (graph.u(e) == graph.v(e) && !allow_loops) continue;
389    int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
390      - weight[e] * mwpfm.dualScale;
391
392    check(rw >= 0, "Negative reduced weight");
393    check(rw == 0 || !mwpfm.matching(e),
394          "Non-zero reduced weight on matching edge");
395  }
396
397  int pv = 0;
398  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
399    int indeg = 0;
400    for (InArcIt a(graph, n); a != INVALID; ++a) {
401      if (mwpfm.matching(graph.source(a)) == a) {
402        ++indeg;
403      }
404    }
405    check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
406    check(indeg == 1, "Invalid perfect matching");
407    pv += weight[mwpfm.matching(n)];
408    SmartGraph::Node o = graph.target(mwpfm.matching(n));
409  }
410
411  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
412    check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +
413          (e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==
414          mwpfm.matching(e), "Invalid matching");
415  }
416
417  int dv = 0;
418  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
419    dv += mwpfm.nodeValue(n);
420  }
421
422  check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
423
424  SmartGraph::NodeMap<bool> processed(graph, false);
425  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
426    if (processed[n]) continue;
427    processed[n] = true;
428    if (mwpfm.matching(n) == INVALID) continue;
429    int num = 1;
430    Node v = graph.target(mwpfm.matching(n));
431    while (v != n) {
432      processed[v] = true;
433      ++num;
434      v = graph.target(mwpfm.matching(v));
435    }
436    check(num == 2 || num % 2 == 1, "Wrong cycle size");
437    check(allow_loops || num != 1, "Wrong cycle size");
438  }
439
440  return;
441}
442
443
444int main() {
445
446  for (int i = 0; i < lgfn; ++i) {
447    SmartGraph graph;
448    SmartGraph::EdgeMap<int> weight(graph);
449
450    istringstream lgfs(lgf[i]);
451    graphReader(graph, lgfs).
452      edgeMap("weight", weight).run();
453
454    bool perfect_with_loops;
455    {
456      MaxFractionalMatching<SmartGraph> mfm(graph, true);
457      mfm.run();
458      checkFractionalMatching(graph, mfm, true);
459      perfect_with_loops = mfm.matchingSize() == countNodes(graph);
460    }
461
462    bool perfect_without_loops;
463    {
464      MaxFractionalMatching<SmartGraph> mfm(graph, false);
465      mfm.run();
466      checkFractionalMatching(graph, mfm, false);
467      perfect_without_loops = mfm.matchingSize() == countNodes(graph);
468    }
469
470    {
471      MaxFractionalMatching<SmartGraph> mfm(graph, true);
472      bool result = mfm.runPerfect();
473      checkPerfectFractionalMatching(graph, mfm, result, true);
474      check(result == perfect_with_loops, "Wrong perfect matching");
475    }
476
477    {
478      MaxFractionalMatching<SmartGraph> mfm(graph, false);
479      bool result = mfm.runPerfect();
480      checkPerfectFractionalMatching(graph, mfm, result, false);
481      check(result == perfect_without_loops, "Wrong perfect matching");
482    }
483
484    {
485      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
486      mwfm.run();
487      checkWeightedFractionalMatching(graph, weight, mwfm, true);
488    }
489
490    {
491      MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
492      mwfm.run();
493      checkWeightedFractionalMatching(graph, weight, mwfm, false);
494    }
495
496    {
497      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
498                                                             true);
499      bool perfect = mwpfm.run();
500      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
501            "Perfect matching found");
502      check(perfect == perfect_with_loops, "Wrong perfect matching");
503
504      if (perfect) {
505        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
506      }
507    }
508
509    {
510      MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
511                                                             false);
512      bool perfect = mwpfm.run();
513      check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
514            "Perfect matching found");
515      check(perfect == perfect_without_loops, "Wrong perfect matching");
516
517      if (perfect) {
518        checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
519      }
520    }
521
522  }
523
524  return 0;
525}
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