deba@948: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@948: *
deba@948: * This file is a part of LEMON, a generic C++ optimization library.
deba@948: *
alpar@956: * Copyright (C) 2003-2010
deba@948: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@948: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@948: *
deba@948: * Permission to use, modify and distribute this software is granted
deba@948: * provided that this copyright notice appears in all copies. For
deba@948: * precise terms see the accompanying LICENSE file.
deba@948: *
deba@948: * This software is provided "AS IS" with no warranty of any kind,
deba@948: * express or implied, and with no claim as to its suitability for any
deba@948: * purpose.
deba@948: *
deba@948: */
deba@948:
deba@948: #include <iostream>
deba@948: #include <sstream>
deba@948: #include <vector>
deba@948: #include <queue>
deba@948: #include <cstdlib>
deba@948:
deba@948: #include <lemon/fractional_matching.h>
deba@948: #include <lemon/smart_graph.h>
deba@948: #include <lemon/concepts/graph.h>
deba@948: #include <lemon/concepts/maps.h>
deba@948: #include <lemon/lgf_reader.h>
deba@948: #include <lemon/math.h>
deba@948:
deba@948: #include "test_tools.h"
deba@948:
deba@948: using namespace std;
deba@948: using namespace lemon;
deba@948:
deba@948: GRAPH_TYPEDEFS(SmartGraph);
deba@948:
deba@948:
deba@948: const int lgfn = 4;
deba@948: const std::string lgf[lgfn] = {
deba@948: "@nodes\n"
deba@948: "label\n"
deba@948: "0\n"
deba@948: "1\n"
deba@948: "2\n"
deba@948: "3\n"
deba@948: "4\n"
deba@948: "5\n"
deba@948: "6\n"
deba@948: "7\n"
deba@948: "@edges\n"
deba@948: " label weight\n"
deba@948: "7 4 0 984\n"
deba@948: "0 7 1 73\n"
deba@948: "7 1 2 204\n"
deba@948: "2 3 3 583\n"
deba@948: "2 7 4 565\n"
deba@948: "2 1 5 582\n"
deba@948: "0 4 6 551\n"
deba@948: "2 5 7 385\n"
deba@948: "1 5 8 561\n"
deba@948: "5 3 9 484\n"
deba@948: "7 5 10 904\n"
deba@948: "3 6 11 47\n"
deba@948: "7 6 12 888\n"
deba@948: "3 0 13 747\n"
deba@948: "6 1 14 310\n",
deba@948:
deba@948: "@nodes\n"
deba@948: "label\n"
deba@948: "0\n"
deba@948: "1\n"
deba@948: "2\n"
deba@948: "3\n"
deba@948: "4\n"
deba@948: "5\n"
deba@948: "6\n"
deba@948: "7\n"
deba@948: "@edges\n"
deba@948: " label weight\n"
deba@948: "2 5 0 710\n"
deba@948: "0 5 1 241\n"
deba@948: "2 4 2 856\n"
deba@948: "2 6 3 762\n"
deba@948: "4 1 4 747\n"
deba@948: "6 1 5 962\n"
deba@948: "4 7 6 723\n"
deba@948: "1 7 7 661\n"
deba@948: "2 3 8 376\n"
deba@948: "1 0 9 416\n"
deba@948: "6 7 10 391\n",
deba@948:
deba@948: "@nodes\n"
deba@948: "label\n"
deba@948: "0\n"
deba@948: "1\n"
deba@948: "2\n"
deba@948: "3\n"
deba@948: "4\n"
deba@948: "5\n"
deba@948: "6\n"
deba@948: "7\n"
deba@948: "@edges\n"
deba@948: " label weight\n"
deba@948: "6 2 0 553\n"
deba@948: "0 7 1 653\n"
deba@948: "6 3 2 22\n"
deba@948: "4 7 3 846\n"
deba@948: "7 2 4 981\n"
deba@948: "7 6 5 250\n"
deba@948: "5 2 6 539\n",
deba@948:
deba@948: "@nodes\n"
deba@948: "label\n"
deba@948: "0\n"
deba@948: "@edges\n"
deba@948: " label weight\n"
deba@948: "0 0 0 100\n"
deba@948: };
deba@948:
deba@948: void checkMaxFractionalMatchingCompile()
deba@948: {
deba@948: typedef concepts::Graph Graph;
deba@948: typedef Graph::Node Node;
deba@948: typedef Graph::Edge Edge;
deba@948:
deba@948: Graph g;
deba@948: Node n;
deba@948: Edge e;
deba@948:
deba@948: MaxFractionalMatching<Graph> mat_test(g);
deba@948: const MaxFractionalMatching<Graph>&
deba@948: const_mat_test = mat_test;
deba@948:
deba@948: mat_test.init();
deba@948: mat_test.start();
deba@948: mat_test.start(true);
deba@948: mat_test.startPerfect();
deba@948: mat_test.startPerfect(true);
deba@948: mat_test.run();
deba@948: mat_test.run(true);
deba@948: mat_test.runPerfect();
deba@948: mat_test.runPerfect(true);
deba@948:
deba@948: const_mat_test.matchingSize();
deba@948: const_mat_test.matching(e);
deba@948: const_mat_test.matching(n);
deba@948: const MaxFractionalMatching<Graph>::MatchingMap& mmap =
deba@948: const_mat_test.matchingMap();
deba@948: e = mmap[n];
deba@948:
deba@948: const_mat_test.barrier(n);
deba@948: }
deba@948:
deba@948: void checkMaxWeightedFractionalMatchingCompile()
deba@948: {
deba@948: typedef concepts::Graph Graph;
deba@948: typedef Graph::Node Node;
deba@948: typedef Graph::Edge Edge;
deba@948: typedef Graph::EdgeMap<int> WeightMap;
deba@948:
deba@948: Graph g;
deba@948: Node n;
deba@948: Edge e;
deba@948: WeightMap w(g);
deba@948:
deba@948: MaxWeightedFractionalMatching<Graph> mat_test(g, w);
deba@948: const MaxWeightedFractionalMatching<Graph>&
deba@948: const_mat_test = mat_test;
deba@948:
deba@948: mat_test.init();
deba@948: mat_test.start();
deba@948: mat_test.run();
deba@948:
deba@948: const_mat_test.matchingWeight();
deba@948: const_mat_test.matchingSize();
deba@948: const_mat_test.matching(e);
deba@948: const_mat_test.matching(n);
deba@948: const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
deba@948: const_mat_test.matchingMap();
deba@948: e = mmap[n];
deba@948:
deba@948: const_mat_test.dualValue();
deba@948: const_mat_test.nodeValue(n);
deba@948: }
deba@948:
deba@948: void checkMaxWeightedPerfectFractionalMatchingCompile()
deba@948: {
deba@948: typedef concepts::Graph Graph;
deba@948: typedef Graph::Node Node;
deba@948: typedef Graph::Edge Edge;
deba@948: typedef Graph::EdgeMap<int> WeightMap;
deba@948:
deba@948: Graph g;
deba@948: Node n;
deba@948: Edge e;
deba@948: WeightMap w(g);
deba@948:
deba@948: MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
deba@948: const MaxWeightedPerfectFractionalMatching<Graph>&
deba@948: const_mat_test = mat_test;
deba@948:
deba@948: mat_test.init();
deba@948: mat_test.start();
deba@948: mat_test.run();
deba@948:
deba@948: const_mat_test.matchingWeight();
deba@948: const_mat_test.matching(e);
deba@948: const_mat_test.matching(n);
deba@948: const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
deba@948: const_mat_test.matchingMap();
deba@948: e = mmap[n];
deba@948:
deba@948: const_mat_test.dualValue();
deba@948: const_mat_test.nodeValue(n);
deba@948: }
deba@948:
deba@948: void checkFractionalMatching(const SmartGraph& graph,
deba@948: const MaxFractionalMatching<SmartGraph>& mfm,
deba@948: bool allow_loops = true) {
deba@948: int pv = 0;
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: int indeg = 0;
deba@948: for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: if (mfm.matching(graph.source(a)) == a) {
deba@948: ++indeg;
deba@948: }
deba@948: }
deba@948: if (mfm.matching(n) != INVALID) {
deba@948: check(indeg == 1, "Invalid matching");
deba@948: ++pv;
deba@948: } else {
deba@948: check(indeg == 0, "Invalid matching");
deba@948: }
deba@948: }
deba@948: check(pv == mfm.matchingSize(), "Wrong matching size");
deba@948:
deba@951: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@951: check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
alpar@956: (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
deba@951: mfm.matching(e), "Invalid matching");
deba@951: }
deba@951:
deba@948: SmartGraph::NodeMap<bool> processed(graph, false);
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: if (processed[n]) continue;
deba@948: processed[n] = true;
deba@948: if (mfm.matching(n) == INVALID) continue;
deba@948: int num = 1;
deba@948: Node v = graph.target(mfm.matching(n));
deba@948: while (v != n) {
deba@948: processed[v] = true;
deba@948: ++num;
deba@948: v = graph.target(mfm.matching(v));
deba@948: }
deba@948: check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@948: check(allow_loops || num != 1, "Wrong cycle size");
deba@948: }
deba@948:
deba@948: int anum = 0, bnum = 0;
deba@948: SmartGraph::NodeMap<bool> neighbours(graph, false);
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: if (!mfm.barrier(n)) continue;
deba@948: ++anum;
deba@948: for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: Node u = graph.source(a);
deba@948: if (!allow_loops && u == n) continue;
deba@948: if (!neighbours[u]) {
deba@948: neighbours[u] = true;
deba@948: ++bnum;
deba@948: }
deba@948: }
deba@948: }
deba@948: check(anum - bnum + mfm.matchingSize() == countNodes(graph),
deba@948: "Wrong barrier");
deba@948: }
deba@948:
deba@948: void checkPerfectFractionalMatching(const SmartGraph& graph,
deba@948: const MaxFractionalMatching<SmartGraph>& mfm,
deba@948: bool perfect, bool allow_loops = true) {
deba@948: if (perfect) {
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: int indeg = 0;
deba@948: for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: if (mfm.matching(graph.source(a)) == a) {
deba@948: ++indeg;
deba@948: }
deba@948: }
deba@948: check(mfm.matching(n) != INVALID, "Invalid matching");
deba@948: check(indeg == 1, "Invalid matching");
deba@948: }
deba@951: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@951: check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
alpar@956: (e == mfm.matching(graph.v(e)) ? 1 : 0) ==
deba@951: mfm.matching(e), "Invalid matching");
deba@951: }
deba@948: } else {
deba@948: int anum = 0, bnum = 0;
deba@948: SmartGraph::NodeMap<bool> neighbours(graph, false);
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: if (!mfm.barrier(n)) continue;
deba@948: ++anum;
deba@948: for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: Node u = graph.source(a);
deba@948: if (!allow_loops && u == n) continue;
deba@948: if (!neighbours[u]) {
deba@948: neighbours[u] = true;
deba@948: ++bnum;
deba@948: }
deba@948: }
deba@948: }
deba@948: check(anum - bnum > 0, "Wrong barrier");
deba@948: }
deba@948: }
deba@948:
deba@948: void checkWeightedFractionalMatching(const SmartGraph& graph,
deba@948: const SmartGraph::EdgeMap<int>& weight,
deba@948: const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
deba@948: bool allow_loops = true) {
deba@948: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@948: if (graph.u(e) == graph.v(e) && !allow_loops) continue;
deba@948: int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
deba@948: - weight[e] * mwfm.dualScale;
deba@948:
deba@948: check(rw >= 0, "Negative reduced weight");
deba@948: check(rw == 0 || !mwfm.matching(e),
deba@948: "Non-zero reduced weight on matching edge");
deba@948: }
deba@948:
deba@948: int pv = 0;
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: int indeg = 0;
deba@948: for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: if (mwfm.matching(graph.source(a)) == a) {
deba@948: ++indeg;
deba@948: }
deba@948: }
deba@948: check(indeg <= 1, "Invalid matching");
deba@948: if (mwfm.matching(n) != INVALID) {
deba@948: check(mwfm.nodeValue(n) >= 0, "Invalid node value");
deba@948: check(indeg == 1, "Invalid matching");
deba@948: pv += weight[mwfm.matching(n)];
deba@948: SmartGraph::Node o = graph.target(mwfm.matching(n));
deba@948: } else {
deba@948: check(mwfm.nodeValue(n) == 0, "Invalid matching");
deba@948: check(indeg == 0, "Invalid matching");
deba@948: }
deba@948: }
deba@948:
deba@951: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@951: check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +
alpar@956: (e == mwfm.matching(graph.v(e)) ? 1 : 0) ==
deba@951: mwfm.matching(e), "Invalid matching");
deba@951: }
deba@951:
deba@948: int dv = 0;
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: dv += mwfm.nodeValue(n);
deba@948: }
deba@948:
deba@948: check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
deba@948:
deba@948: SmartGraph::NodeMap<bool> processed(graph, false);
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: if (processed[n]) continue;
deba@948: processed[n] = true;
deba@948: if (mwfm.matching(n) == INVALID) continue;
deba@948: int num = 1;
deba@948: Node v = graph.target(mwfm.matching(n));
deba@948: while (v != n) {
deba@948: processed[v] = true;
deba@948: ++num;
deba@948: v = graph.target(mwfm.matching(v));
deba@948: }
deba@948: check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@948: check(allow_loops || num != 1, "Wrong cycle size");
deba@948: }
deba@948:
deba@948: return;
deba@948: }
deba@948:
deba@948: void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
deba@948: const SmartGraph::EdgeMap<int>& weight,
deba@948: const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
deba@948: bool allow_loops = true) {
deba@948: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@948: if (graph.u(e) == graph.v(e) && !allow_loops) continue;
deba@948: int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
deba@948: - weight[e] * mwpfm.dualScale;
deba@948:
deba@948: check(rw >= 0, "Negative reduced weight");
deba@948: check(rw == 0 || !mwpfm.matching(e),
deba@948: "Non-zero reduced weight on matching edge");
deba@948: }
deba@948:
deba@948: int pv = 0;
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: int indeg = 0;
deba@948: for (InArcIt a(graph, n); a != INVALID; ++a) {
deba@948: if (mwpfm.matching(graph.source(a)) == a) {
deba@948: ++indeg;
deba@948: }
deba@948: }
deba@948: check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
deba@948: check(indeg == 1, "Invalid perfect matching");
deba@948: pv += weight[mwpfm.matching(n)];
deba@948: SmartGraph::Node o = graph.target(mwpfm.matching(n));
deba@948: }
deba@948:
deba@951: for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
deba@951: check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +
alpar@956: (e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==
deba@951: mwpfm.matching(e), "Invalid matching");
deba@951: }
deba@951:
deba@948: int dv = 0;
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: dv += mwpfm.nodeValue(n);
deba@948: }
deba@948:
deba@948: check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
deba@948:
deba@948: SmartGraph::NodeMap<bool> processed(graph, false);
deba@948: for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
deba@948: if (processed[n]) continue;
deba@948: processed[n] = true;
deba@948: if (mwpfm.matching(n) == INVALID) continue;
deba@948: int num = 1;
deba@948: Node v = graph.target(mwpfm.matching(n));
deba@948: while (v != n) {
deba@948: processed[v] = true;
deba@948: ++num;
deba@948: v = graph.target(mwpfm.matching(v));
deba@948: }
deba@948: check(num == 2 || num % 2 == 1, "Wrong cycle size");
deba@948: check(allow_loops || num != 1, "Wrong cycle size");
deba@948: }
deba@948:
deba@948: return;
deba@948: }
deba@948:
deba@948:
deba@948: int main() {
deba@948:
deba@948: for (int i = 0; i < lgfn; ++i) {
deba@948: SmartGraph graph;
deba@948: SmartGraph::EdgeMap<int> weight(graph);
deba@948:
deba@948: istringstream lgfs(lgf[i]);
deba@948: graphReader(graph, lgfs).
deba@948: edgeMap("weight", weight).run();
deba@948:
deba@948: bool perfect_with_loops;
deba@948: {
deba@948: MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@948: mfm.run();
deba@948: checkFractionalMatching(graph, mfm, true);
deba@948: perfect_with_loops = mfm.matchingSize() == countNodes(graph);
deba@948: }
deba@948:
deba@948: bool perfect_without_loops;
deba@948: {
deba@948: MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@948: mfm.run();
deba@948: checkFractionalMatching(graph, mfm, false);
deba@948: perfect_without_loops = mfm.matchingSize() == countNodes(graph);
deba@948: }
deba@948:
deba@948: {
deba@948: MaxFractionalMatching<SmartGraph> mfm(graph, true);
deba@948: bool result = mfm.runPerfect();
deba@948: checkPerfectFractionalMatching(graph, mfm, result, true);
deba@948: check(result == perfect_with_loops, "Wrong perfect matching");
deba@948: }
deba@948:
deba@948: {
deba@948: MaxFractionalMatching<SmartGraph> mfm(graph, false);
deba@948: bool result = mfm.runPerfect();
deba@948: checkPerfectFractionalMatching(graph, mfm, result, false);
deba@948: check(result == perfect_without_loops, "Wrong perfect matching");
deba@948: }
deba@948:
deba@948: {
deba@948: MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
deba@948: mwfm.run();
deba@948: checkWeightedFractionalMatching(graph, weight, mwfm, true);
deba@948: }
deba@948:
deba@948: {
deba@948: MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
deba@948: mwfm.run();
deba@948: checkWeightedFractionalMatching(graph, weight, mwfm, false);
deba@948: }
deba@948:
deba@948: {
deba@948: MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@948: true);
deba@948: bool perfect = mwpfm.run();
deba@948: check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@948: "Perfect matching found");
deba@948: check(perfect == perfect_with_loops, "Wrong perfect matching");
deba@948:
deba@948: if (perfect) {
deba@948: checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
deba@948: }
deba@948: }
deba@948:
deba@948: {
deba@948: MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
deba@948: false);
deba@948: bool perfect = mwpfm.run();
deba@948: check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
deba@948: "Perfect matching found");
deba@948: check(perfect == perfect_without_loops, "Wrong perfect matching");
deba@948:
deba@948: if (perfect) {
deba@948: checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
deba@948: }
deba@948: }
deba@948:
deba@948: }
deba@948:
deba@948: return 0;
deba@948: }