1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/test/max_matching_test.cc Wed Oct 22 14:41:18 2008 +0100
1.3 @@ -0,0 +1,310 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2008
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#include <iostream>
1.23 +#include <sstream>
1.24 +#include <vector>
1.25 +#include <queue>
1.26 +#include <lemon/math.h>
1.27 +#include <cstdlib>
1.28 +
1.29 +#include <lemon/max_matching.h>
1.30 +#include <lemon/smart_graph.h>
1.31 +#include <lemon/lgf_reader.h>
1.32 +
1.33 +#include "test_tools.h"
1.34 +
1.35 +using namespace std;
1.36 +using namespace lemon;
1.37 +
1.38 +GRAPH_TYPEDEFS(SmartGraph);
1.39 +
1.40 +
1.41 +const int lgfn = 3;
1.42 +const std::string lgf[lgfn] = {
1.43 + "@nodes\n"
1.44 + "label\n"
1.45 + "0\n"
1.46 + "1\n"
1.47 + "2\n"
1.48 + "3\n"
1.49 + "4\n"
1.50 + "5\n"
1.51 + "6\n"
1.52 + "7\n"
1.53 + "@edges\n"
1.54 + " label weight\n"
1.55 + "7 4 0 984\n"
1.56 + "0 7 1 73\n"
1.57 + "7 1 2 204\n"
1.58 + "2 3 3 583\n"
1.59 + "2 7 4 565\n"
1.60 + "2 1 5 582\n"
1.61 + "0 4 6 551\n"
1.62 + "2 5 7 385\n"
1.63 + "1 5 8 561\n"
1.64 + "5 3 9 484\n"
1.65 + "7 5 10 904\n"
1.66 + "3 6 11 47\n"
1.67 + "7 6 12 888\n"
1.68 + "3 0 13 747\n"
1.69 + "6 1 14 310\n",
1.70 +
1.71 + "@nodes\n"
1.72 + "label\n"
1.73 + "0\n"
1.74 + "1\n"
1.75 + "2\n"
1.76 + "3\n"
1.77 + "4\n"
1.78 + "5\n"
1.79 + "6\n"
1.80 + "7\n"
1.81 + "@edges\n"
1.82 + " label weight\n"
1.83 + "2 5 0 710\n"
1.84 + "0 5 1 241\n"
1.85 + "2 4 2 856\n"
1.86 + "2 6 3 762\n"
1.87 + "4 1 4 747\n"
1.88 + "6 1 5 962\n"
1.89 + "4 7 6 723\n"
1.90 + "1 7 7 661\n"
1.91 + "2 3 8 376\n"
1.92 + "1 0 9 416\n"
1.93 + "6 7 10 391\n",
1.94 +
1.95 + "@nodes\n"
1.96 + "label\n"
1.97 + "0\n"
1.98 + "1\n"
1.99 + "2\n"
1.100 + "3\n"
1.101 + "4\n"
1.102 + "5\n"
1.103 + "6\n"
1.104 + "7\n"
1.105 + "@edges\n"
1.106 + " label weight\n"
1.107 + "6 2 0 553\n"
1.108 + "0 7 1 653\n"
1.109 + "6 3 2 22\n"
1.110 + "4 7 3 846\n"
1.111 + "7 2 4 981\n"
1.112 + "7 6 5 250\n"
1.113 + "5 2 6 539\n",
1.114 +};
1.115 +
1.116 +void checkMatching(const SmartGraph& graph,
1.117 + const MaxMatching<SmartGraph>& mm) {
1.118 + int num = 0;
1.119 +
1.120 + IntNodeMap comp_index(graph);
1.121 + UnionFind<IntNodeMap> comp(comp_index);
1.122 +
1.123 + int barrier_num = 0;
1.124 +
1.125 + for (NodeIt n(graph); n != INVALID; ++n) {
1.126 + check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
1.127 + mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
1.128 + if (mm.decomposition(n) == MaxMatching<SmartGraph>::ODD) {
1.129 + ++barrier_num;
1.130 + } else {
1.131 + comp.insert(n);
1.132 + }
1.133 + }
1.134 +
1.135 + for (EdgeIt e(graph); e != INVALID; ++e) {
1.136 + if (mm.matching(e)) {
1.137 + check(e == mm.matching(graph.u(e)), "Wrong matching");
1.138 + check(e == mm.matching(graph.v(e)), "Wrong matching");
1.139 + ++num;
1.140 + }
1.141 + check(mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
1.142 + mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
1.143 + "Wrong Gallai-Edmonds decomposition");
1.144 +
1.145 + check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
1.146 + mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
1.147 + "Wrong Gallai-Edmonds decomposition");
1.148 +
1.149 + if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
1.150 + mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
1.151 + comp.join(graph.u(e), graph.v(e));
1.152 + }
1.153 + }
1.154 +
1.155 + std::set<int> comp_root;
1.156 + int odd_comp_num = 0;
1.157 + for (NodeIt n(graph); n != INVALID; ++n) {
1.158 + if (mm.decomposition(n) != MaxMatching<SmartGraph>::ODD) {
1.159 + int root = comp.find(n);
1.160 + if (comp_root.find(root) == comp_root.end()) {
1.161 + comp_root.insert(root);
1.162 + if (comp.size(n) % 2 == 1) {
1.163 + ++odd_comp_num;
1.164 + }
1.165 + }
1.166 + }
1.167 + }
1.168 +
1.169 + check(mm.matchingSize() == num, "Wrong matching");
1.170 + check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num),
1.171 + "Wrong matching");
1.172 + return;
1.173 +}
1.174 +
1.175 +void checkWeightedMatching(const SmartGraph& graph,
1.176 + const SmartGraph::EdgeMap<int>& weight,
1.177 + const MaxWeightedMatching<SmartGraph>& mwm) {
1.178 + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
1.179 + if (graph.u(e) == graph.v(e)) continue;
1.180 + int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e));
1.181 +
1.182 + for (int i = 0; i < mwm.blossomNum(); ++i) {
1.183 + bool s = false, t = false;
1.184 + for (MaxWeightedMatching<SmartGraph>::BlossomIt n(mwm, i);
1.185 + n != INVALID; ++n) {
1.186 + if (graph.u(e) == n) s = true;
1.187 + if (graph.v(e) == n) t = true;
1.188 + }
1.189 + if (s == true && t == true) {
1.190 + rw += mwm.blossomValue(i);
1.191 + }
1.192 + }
1.193 + rw -= weight[e] * mwm.dualScale;
1.194 +
1.195 + check(rw >= 0, "Negative reduced weight");
1.196 + check(rw == 0 || !mwm.matching(e),
1.197 + "Non-zero reduced weight on matching edge");
1.198 + }
1.199 +
1.200 + int pv = 0;
1.201 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
1.202 + if (mwm.matching(n) != INVALID) {
1.203 + check(mwm.nodeValue(n) >= 0, "Invalid node value");
1.204 + pv += weight[mwm.matching(n)];
1.205 + SmartGraph::Node o = graph.target(mwm.matching(n));
1.206 + check(mwm.mate(n) == o, "Invalid matching");
1.207 + check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)),
1.208 + "Invalid matching");
1.209 + } else {
1.210 + check(mwm.mate(n) == INVALID, "Invalid matching");
1.211 + check(mwm.nodeValue(n) == 0, "Invalid matching");
1.212 + }
1.213 + }
1.214 +
1.215 + int dv = 0;
1.216 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
1.217 + dv += mwm.nodeValue(n);
1.218 + }
1.219 +
1.220 + for (int i = 0; i < mwm.blossomNum(); ++i) {
1.221 + check(mwm.blossomValue(i) >= 0, "Invalid blossom value");
1.222 + check(mwm.blossomSize(i) % 2 == 1, "Even blossom size");
1.223 + dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2);
1.224 + }
1.225 +
1.226 + check(pv * mwm.dualScale == dv * 2, "Wrong duality");
1.227 +
1.228 + return;
1.229 +}
1.230 +
1.231 +void checkWeightedPerfectMatching(const SmartGraph& graph,
1.232 + const SmartGraph::EdgeMap<int>& weight,
1.233 + const MaxWeightedPerfectMatching<SmartGraph>& mwpm) {
1.234 + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
1.235 + if (graph.u(e) == graph.v(e)) continue;
1.236 + int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e));
1.237 +
1.238 + for (int i = 0; i < mwpm.blossomNum(); ++i) {
1.239 + bool s = false, t = false;
1.240 + for (MaxWeightedPerfectMatching<SmartGraph>::BlossomIt n(mwpm, i);
1.241 + n != INVALID; ++n) {
1.242 + if (graph.u(e) == n) s = true;
1.243 + if (graph.v(e) == n) t = true;
1.244 + }
1.245 + if (s == true && t == true) {
1.246 + rw += mwpm.blossomValue(i);
1.247 + }
1.248 + }
1.249 + rw -= weight[e] * mwpm.dualScale;
1.250 +
1.251 + check(rw >= 0, "Negative reduced weight");
1.252 + check(rw == 0 || !mwpm.matching(e),
1.253 + "Non-zero reduced weight on matching edge");
1.254 + }
1.255 +
1.256 + int pv = 0;
1.257 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
1.258 + check(mwpm.matching(n) != INVALID, "Non perfect");
1.259 + pv += weight[mwpm.matching(n)];
1.260 + SmartGraph::Node o = graph.target(mwpm.matching(n));
1.261 + check(mwpm.mate(n) == o, "Invalid matching");
1.262 + check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)),
1.263 + "Invalid matching");
1.264 + }
1.265 +
1.266 + int dv = 0;
1.267 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
1.268 + dv += mwpm.nodeValue(n);
1.269 + }
1.270 +
1.271 + for (int i = 0; i < mwpm.blossomNum(); ++i) {
1.272 + check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");
1.273 + check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");
1.274 + dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);
1.275 + }
1.276 +
1.277 + check(pv * mwpm.dualScale == dv * 2, "Wrong duality");
1.278 +
1.279 + return;
1.280 +}
1.281 +
1.282 +
1.283 +int main() {
1.284 +
1.285 + for (int i = 0; i < lgfn; ++i) {
1.286 + SmartGraph graph;
1.287 + SmartGraph::EdgeMap<int> weight(graph);
1.288 +
1.289 + istringstream lgfs(lgf[i]);
1.290 + graphReader(graph, lgfs).
1.291 + edgeMap("weight", weight).run();
1.292 +
1.293 + MaxMatching<SmartGraph> mm(graph);
1.294 + mm.run();
1.295 + checkMatching(graph, mm);
1.296 +
1.297 + MaxWeightedMatching<SmartGraph> mwm(graph, weight);
1.298 + mwm.run();
1.299 + checkWeightedMatching(graph, weight, mwm);
1.300 +
1.301 + MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
1.302 + bool perfect = mwpm.run();
1.303 +
1.304 + check(perfect == (mm.matchingSize() * 2 == countNodes(graph)),
1.305 + "Perfect matching found");
1.306 +
1.307 + if (perfect) {
1.308 + checkWeightedPerfectMatching(graph, weight, mwpm);
1.309 + }
1.310 + }
1.311 +
1.312 + return 0;
1.313 +}