COIN-OR::LEMON - Graph Library

source: lemon/test/max_matching_test.cc @ 442:ff48c2738fb2

Last change on this file since 442:ff48c2738fb2 was 339:91d63b8b1a4c, checked in by Balazs Dezso <deba@…>, 11 years ago

Several improvements in maximum matching algorithms

  • The interface of MaxMatching? is changed to be similar to the weighted algorithms
  • The internal data structure (the queue implementation and the matching map) is changed in the MaxMatching? algorithm, which provides better runtime properties
  • The Blossom iterators are changed slightly in the weighted matching algorithms
  • Several documentation improvments
  • The test files are merged
File size: 8.1 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) 2003-2008
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 <lemon/math.h>
24#include <cstdlib>
25
26#include <lemon/max_matching.h>
27#include <lemon/smart_graph.h>
28#include <lemon/lgf_reader.h>
29
30#include "test_tools.h"
31
32using namespace std;
33using namespace lemon;
34
35GRAPH_TYPEDEFS(SmartGraph);
36
37
38const int lgfn = 3;
39const std::string lgf[lgfn] = {
40  "@nodes\n"
41  "label\n"
42  "0\n"
43  "1\n"
44  "2\n"
45  "3\n"
46  "4\n"
47  "5\n"
48  "6\n"
49  "7\n"
50  "@edges\n"
51  "     label  weight\n"
52  "7 4  0      984\n"
53  "0 7  1      73\n"
54  "7 1  2      204\n"
55  "2 3  3      583\n"
56  "2 7  4      565\n"
57  "2 1  5      582\n"
58  "0 4  6      551\n"
59  "2 5  7      385\n"
60  "1 5  8      561\n"
61  "5 3  9      484\n"
62  "7 5  10     904\n"
63  "3 6  11     47\n"
64  "7 6  12     888\n"
65  "3 0  13     747\n"
66  "6 1  14     310\n",
67
68  "@nodes\n"
69  "label\n"
70  "0\n"
71  "1\n"
72  "2\n"
73  "3\n"
74  "4\n"
75  "5\n"
76  "6\n"
77  "7\n"
78  "@edges\n"
79  "     label  weight\n"
80  "2 5  0      710\n"
81  "0 5  1      241\n"
82  "2 4  2      856\n"
83  "2 6  3      762\n"
84  "4 1  4      747\n"
85  "6 1  5      962\n"
86  "4 7  6      723\n"
87  "1 7  7      661\n"
88  "2 3  8      376\n"
89  "1 0  9      416\n"
90  "6 7  10     391\n",
91
92  "@nodes\n"
93  "label\n"
94  "0\n"
95  "1\n"
96  "2\n"
97  "3\n"
98  "4\n"
99  "5\n"
100  "6\n"
101  "7\n"
102  "@edges\n"
103  "     label  weight\n"
104  "6 2  0      553\n"
105  "0 7  1      653\n"
106  "6 3  2      22\n"
107  "4 7  3      846\n"
108  "7 2  4      981\n"
109  "7 6  5      250\n"
110  "5 2  6      539\n",
111};
112
113void checkMatching(const SmartGraph& graph,
114                   const MaxMatching<SmartGraph>& mm) {
115  int num = 0;
116
117  IntNodeMap comp_index(graph);
118  UnionFind<IntNodeMap> comp(comp_index);
119
120  int barrier_num = 0;
121
122  for (NodeIt n(graph); n != INVALID; ++n) {
123    check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
124          mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
125    if (mm.decomposition(n) == MaxMatching<SmartGraph>::ODD) {
126      ++barrier_num;
127    } else {
128      comp.insert(n);
129    }
130  }
131
132  for (EdgeIt e(graph); e != INVALID; ++e) {
133    if (mm.matching(e)) {
134      check(e == mm.matching(graph.u(e)), "Wrong matching");
135      check(e == mm.matching(graph.v(e)), "Wrong matching");
136      ++num;
137    }
138    check(mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
139          mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
140          "Wrong Gallai-Edmonds decomposition");
141
142    check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
143          mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
144          "Wrong Gallai-Edmonds decomposition");
145
146    if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
147        mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
148      comp.join(graph.u(e), graph.v(e));
149    }
150  }
151
152  std::set<int> comp_root;
153  int odd_comp_num = 0;
154  for (NodeIt n(graph); n != INVALID; ++n) {
155    if (mm.decomposition(n) != MaxMatching<SmartGraph>::ODD) {
156      int root = comp.find(n);
157      if (comp_root.find(root) == comp_root.end()) {
158        comp_root.insert(root);
159        if (comp.size(n) % 2 == 1) {
160          ++odd_comp_num;
161        }
162      }
163    }
164  }
165
166  check(mm.matchingSize() == num, "Wrong matching");
167  check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
168         "Wrong matching");
169  return;
170}
171
172void checkWeightedMatching(const SmartGraph& graph,
173                   const SmartGraph::EdgeMap<int>& weight,
174                   const MaxWeightedMatching<SmartGraph>& mwm) {
175  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
176    if (graph.u(e) == graph.v(e)) continue;
177    int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
178
179    for (int i = 0; i < mwm.blossomNum(); ++i) {
180      bool s = false, t = false;
181      for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
182           n != INVALID; ++n) {
183        if (graph.u(e) == n) s = true;
184        if (graph.v(e) == n) t = true;
185      }
186      if (s == true && t == true) {
187        rw += mwm.blossomValue(i);
188      }
189    }
190    rw -= weight[e] * mwm.dualScale;
191
192    check(rw >= 0, "Negative reduced weight");
193    check(rw == 0 || !mwm.matching(e),
194          "Non-zero reduced weight on matching edge");
195  }
196
197  int pv = 0;
198  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
199    if (mwm.matching(n) != INVALID) {
200      check(mwm.nodeValue(n) >= 0, "Invalid node value");
201      pv += weight[mwm.matching(n)];
202      SmartGraph::Node o = graph.target(mwm.matching(n));
203      check(mwm.mate(n) == o, "Invalid matching");
204      check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
205            "Invalid matching");
206    } else {
207      check(mwm.mate(n) == INVALID, "Invalid matching");
208      check(mwm.nodeValue(n) == 0, "Invalid matching");
209    }
210  }
211
212  int dv = 0;
213  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
214    dv += mwm.nodeValue(n);
215  }
216
217  for (int i = 0; i < mwm.blossomNum(); ++i) {
218    check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
219    check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
220    dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
221  }
222
223  check(pv * mwm.dualScale == dv * 2, "Wrong duality");
224
225  return;
226}
227
228void checkWeightedPerfectMatching(const SmartGraph& graph,
229                          const SmartGraph::EdgeMap<int>& weight,
230                          const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
231  for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
232    if (graph.u(e) == graph.v(e)) continue;
233    int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
234
235    for (int i = 0; i < mwpm.blossomNum(); ++i) {
236      bool s = false, t = false;
237      for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
238           n != INVALID; ++n) {
239        if (graph.u(e) == n) s = true;
240        if (graph.v(e) == n) t = true;
241      }
242      if (s == true && t == true) {
243        rw += mwpm.blossomValue(i);
244      }
245    }
246    rw -= weight[e] * mwpm.dualScale;
247
248    check(rw >= 0, "Negative reduced weight");
249    check(rw == 0 || !mwpm.matching(e),
250          "Non-zero reduced weight on matching edge");
251  }
252
253  int pv = 0;
254  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
255    check(mwpm.matching(n) != INVALID, "Non perfect");
256    pv += weight[mwpm.matching(n)];
257    SmartGraph::Node o = graph.target(mwpm.matching(n));
258    check(mwpm.mate(n) == o, "Invalid matching");
259    check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
260          "Invalid matching");
261  }
262
263  int dv = 0;
264  for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
265    dv += mwpm.nodeValue(n);
266  }
267
268  for (int i = 0; i < mwpm.blossomNum(); ++i) {
269    check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
270    check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
271    dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
272  }
273
274  check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
275
276  return;
277}
278
279
280int main() {
281
282  for (int i = 0; i < lgfn; ++i) {
283    SmartGraph graph;
284    SmartGraph::EdgeMap<int> weight(graph);
285
286    istringstream lgfs(lgf[i]);
287    graphReader(graph, lgfs).
288      edgeMap("weight", weight).run();
289
290    MaxMatching<SmartGraph> mm(graph);
291    mm.run();
292    checkMatching(graph, mm);
293
294    MaxWeightedMatching<SmartGraph> mwm(graph, weight);
295    mwm.run();
296    checkWeightedMatching(graph, weight, mwm);
297
298    MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
299    bool perfect = mwpm.run();
300
301    check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
302          "Perfect matching found");
303
304    if (perfect) {
305      checkWeightedPerfectMatching(graph, weight, mwpm);
306    }
307  }
308
309  return 0;
310}
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