diff --git a/test/matching_test.cc b/test/matching_test.cc new file mode 100644 --- /dev/null +++ b/test/matching_test.cc @@ -0,0 +1,424 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include + +#include "test_tools.h" + +using namespace std; +using namespace lemon; + +GRAPH_TYPEDEFS(SmartGraph); + + +const int lgfn = 3; +const std::string lgf[lgfn] = { + "@nodes\n" + "label\n" + "0\n" + "1\n" + "2\n" + "3\n" + "4\n" + "5\n" + "6\n" + "7\n" + "@edges\n" + " label weight\n" + "7 4 0 984\n" + "0 7 1 73\n" + "7 1 2 204\n" + "2 3 3 583\n" + "2 7 4 565\n" + "2 1 5 582\n" + "0 4 6 551\n" + "2 5 7 385\n" + "1 5 8 561\n" + "5 3 9 484\n" + "7 5 10 904\n" + "3 6 11 47\n" + "7 6 12 888\n" + "3 0 13 747\n" + "6 1 14 310\n", + + "@nodes\n" + "label\n" + "0\n" + "1\n" + "2\n" + "3\n" + "4\n" + "5\n" + "6\n" + "7\n" + "@edges\n" + " label weight\n" + "2 5 0 710\n" + "0 5 1 241\n" + "2 4 2 856\n" + "2 6 3 762\n" + "4 1 4 747\n" + "6 1 5 962\n" + "4 7 6 723\n" + "1 7 7 661\n" + "2 3 8 376\n" + "1 0 9 416\n" + "6 7 10 391\n", + + "@nodes\n" + "label\n" + "0\n" + "1\n" + "2\n" + "3\n" + "4\n" + "5\n" + "6\n" + "7\n" + "@edges\n" + " label weight\n" + "6 2 0 553\n" + "0 7 1 653\n" + "6 3 2 22\n" + "4 7 3 846\n" + "7 2 4 981\n" + "7 6 5 250\n" + "5 2 6 539\n", +}; + +void checkMaxMatchingCompile() +{ + typedef concepts::Graph Graph; + typedef Graph::Node Node; + typedef Graph::Edge Edge; + typedef Graph::EdgeMap MatMap; + + Graph g; + Node n; + Edge e; + MatMap mat(g); + + MaxMatching mat_test(g); + const MaxMatching& + const_mat_test = mat_test; + + mat_test.init(); + mat_test.greedyInit(); + mat_test.matchingInit(mat); + mat_test.startSparse(); + mat_test.startDense(); + mat_test.run(); + + const_mat_test.matchingSize(); + const_mat_test.matching(e); + const_mat_test.matching(n); + const MaxMatching::MatchingMap& mmap = + const_mat_test.matchingMap(); + e = mmap[n]; + const_mat_test.mate(n); + + MaxMatching::Status stat = + const_mat_test.status(n); + const MaxMatching::StatusMap& smap = + const_mat_test.statusMap(); + stat = smap[n]; + const_mat_test.barrier(n); +} + +void checkMaxWeightedMatchingCompile() +{ + typedef concepts::Graph Graph; + typedef Graph::Node Node; + typedef Graph::Edge Edge; + typedef Graph::EdgeMap WeightMap; + + Graph g; + Node n; + Edge e; + WeightMap w(g); + + MaxWeightedMatching mat_test(g, w); + const MaxWeightedMatching& + const_mat_test = mat_test; + + mat_test.init(); + mat_test.start(); + mat_test.run(); + + const_mat_test.matchingWeight(); + const_mat_test.matchingSize(); + const_mat_test.matching(e); + const_mat_test.matching(n); + const MaxWeightedMatching::MatchingMap& mmap = + const_mat_test.matchingMap(); + e = mmap[n]; + const_mat_test.mate(n); + + int k = 0; + const_mat_test.dualValue(); + const_mat_test.nodeValue(n); + const_mat_test.blossomNum(); + const_mat_test.blossomSize(k); + const_mat_test.blossomValue(k); +} + +void checkMaxWeightedPerfectMatchingCompile() +{ + typedef concepts::Graph Graph; + typedef Graph::Node Node; + typedef Graph::Edge Edge; + typedef Graph::EdgeMap WeightMap; + + Graph g; + Node n; + Edge e; + WeightMap w(g); + + MaxWeightedPerfectMatching mat_test(g, w); + const MaxWeightedPerfectMatching& + const_mat_test = mat_test; + + mat_test.init(); + mat_test.start(); + mat_test.run(); + + const_mat_test.matchingWeight(); + const_mat_test.matching(e); + const_mat_test.matching(n); + const MaxWeightedPerfectMatching::MatchingMap& mmap = + const_mat_test.matchingMap(); + e = mmap[n]; + const_mat_test.mate(n); + + int k = 0; + const_mat_test.dualValue(); + const_mat_test.nodeValue(n); + const_mat_test.blossomNum(); + const_mat_test.blossomSize(k); + const_mat_test.blossomValue(k); +} + +void checkMatching(const SmartGraph& graph, + const MaxMatching& mm) { + int num = 0; + + IntNodeMap comp_index(graph); + UnionFind comp(comp_index); + + int barrier_num = 0; + + for (NodeIt n(graph); n != INVALID; ++n) { + check(mm.status(n) == MaxMatching::EVEN || + mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition"); + if (mm.status(n) == MaxMatching::ODD) { + ++barrier_num; + } else { + comp.insert(n); + } + } + + for (EdgeIt e(graph); e != INVALID; ++e) { + if (mm.matching(e)) { + check(e == mm.matching(graph.u(e)), "Wrong matching"); + check(e == mm.matching(graph.v(e)), "Wrong matching"); + ++num; + } + check(mm.status(graph.u(e)) != MaxMatching::EVEN || + mm.status(graph.v(e)) != MaxMatching::MATCHED, + "Wrong Gallai-Edmonds decomposition"); + + check(mm.status(graph.v(e)) != MaxMatching::EVEN || + mm.status(graph.u(e)) != MaxMatching::MATCHED, + "Wrong Gallai-Edmonds decomposition"); + + if (mm.status(graph.u(e)) != MaxMatching::ODD && + mm.status(graph.v(e)) != MaxMatching::ODD) { + comp.join(graph.u(e), graph.v(e)); + } + } + + std::set comp_root; + int odd_comp_num = 0; + for (NodeIt n(graph); n != INVALID; ++n) { + if (mm.status(n) != MaxMatching::ODD) { + int root = comp.find(n); + if (comp_root.find(root) == comp_root.end()) { + comp_root.insert(root); + if (comp.size(n) % 2 == 1) { + ++odd_comp_num; + } + } + } + } + + check(mm.matchingSize() == num, "Wrong matching"); + check(2 * num == countNodes(graph) - (odd_comp_num - barrier_num), + "Wrong matching"); + return; +} + +void checkWeightedMatching(const SmartGraph& graph, + const SmartGraph::EdgeMap& weight, + const MaxWeightedMatching& mwm) { + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { + if (graph.u(e) == graph.v(e)) continue; + int rw = mwm.nodeValue(graph.u(e)) + mwm.nodeValue(graph.v(e)); + + for (int i = 0; i < mwm.blossomNum(); ++i) { + bool s = false, t = false; + for (MaxWeightedMatching::BlossomIt n(mwm, i); + n != INVALID; ++n) { + if (graph.u(e) == n) s = true; + if (graph.v(e) == n) t = true; + } + if (s == true && t == true) { + rw += mwm.blossomValue(i); + } + } + rw -= weight[e] * mwm.dualScale; + + check(rw >= 0, "Negative reduced weight"); + check(rw == 0 || !mwm.matching(e), + "Non-zero reduced weight on matching edge"); + } + + int pv = 0; + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { + if (mwm.matching(n) != INVALID) { + check(mwm.nodeValue(n) >= 0, "Invalid node value"); + pv += weight[mwm.matching(n)]; + SmartGraph::Node o = graph.target(mwm.matching(n)); + check(mwm.mate(n) == o, "Invalid matching"); + check(mwm.matching(n) == graph.oppositeArc(mwm.matching(o)), + "Invalid matching"); + } else { + check(mwm.mate(n) == INVALID, "Invalid matching"); + check(mwm.nodeValue(n) == 0, "Invalid matching"); + } + } + + int dv = 0; + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { + dv += mwm.nodeValue(n); + } + + for (int i = 0; i < mwm.blossomNum(); ++i) { + check(mwm.blossomValue(i) >= 0, "Invalid blossom value"); + check(mwm.blossomSize(i) % 2 == 1, "Even blossom size"); + dv += mwm.blossomValue(i) * ((mwm.blossomSize(i) - 1) / 2); + } + + check(pv * mwm.dualScale == dv * 2, "Wrong duality"); + + return; +} + +void checkWeightedPerfectMatching(const SmartGraph& graph, + const SmartGraph::EdgeMap& weight, + const MaxWeightedPerfectMatching& mwpm) { + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { + if (graph.u(e) == graph.v(e)) continue; + int rw = mwpm.nodeValue(graph.u(e)) + mwpm.nodeValue(graph.v(e)); + + for (int i = 0; i < mwpm.blossomNum(); ++i) { + bool s = false, t = false; + for (MaxWeightedPerfectMatching::BlossomIt n(mwpm, i); + n != INVALID; ++n) { + if (graph.u(e) == n) s = true; + if (graph.v(e) == n) t = true; + } + if (s == true && t == true) { + rw += mwpm.blossomValue(i); + } + } + rw -= weight[e] * mwpm.dualScale; + + check(rw >= 0, "Negative reduced weight"); + check(rw == 0 || !mwpm.matching(e), + "Non-zero reduced weight on matching edge"); + } + + int pv = 0; + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { + check(mwpm.matching(n) != INVALID, "Non perfect"); + pv += weight[mwpm.matching(n)]; + SmartGraph::Node o = graph.target(mwpm.matching(n)); + check(mwpm.mate(n) == o, "Invalid matching"); + check(mwpm.matching(n) == graph.oppositeArc(mwpm.matching(o)), + "Invalid matching"); + } + + int dv = 0; + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { + dv += mwpm.nodeValue(n); + } + + for (int i = 0; i < mwpm.blossomNum(); ++i) { + check(mwpm.blossomValue(i) >= 0, "Invalid blossom value"); + check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size"); + dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2); + } + + check(pv * mwpm.dualScale == dv * 2, "Wrong duality"); + + return; +} + + +int main() { + + for (int i = 0; i < lgfn; ++i) { + SmartGraph graph; + SmartGraph::EdgeMap weight(graph); + + istringstream lgfs(lgf[i]); + graphReader(graph, lgfs). + edgeMap("weight", weight).run(); + + MaxMatching mm(graph); + mm.run(); + checkMatching(graph, mm); + + MaxWeightedMatching mwm(graph, weight); + mwm.run(); + checkWeightedMatching(graph, weight, mwm); + + MaxWeightedPerfectMatching mwpm(graph, weight); + bool perfect = mwpm.run(); + + check(perfect == (mm.matchingSize() * 2 == countNodes(graph)), + "Perfect matching found"); + + if (perfect) { + checkWeightedPerfectMatching(graph, weight, mwpm); + } + } + + return 0; +}