528 lines
14 KiB
C++
528 lines
14 KiB
C++
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2013
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#include <iostream>
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#include <sstream>
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#include <vector>
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#include <queue>
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#include <cstdlib>
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#include <lemon/fractional_matching.h>
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#include <lemon/smart_graph.h>
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#include <lemon/concepts/graph.h>
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#include <lemon/concepts/maps.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/math.h>
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#include "test_tools.h"
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using namespace std;
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using namespace lemon;
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GRAPH_TYPEDEFS(SmartGraph);
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const int lgfn = 4;
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const std::string lgf[lgfn] = {
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"@nodes\n"
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"label\n"
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"0\n"
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"1\n"
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"2\n"
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"3\n"
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"4\n"
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"5\n"
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"6\n"
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"7\n"
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"@edges\n"
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" label weight\n"
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"7 4 0 984\n"
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"0 7 1 73\n"
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"7 1 2 204\n"
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"2 3 3 583\n"
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"2 7 4 565\n"
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"2 1 5 582\n"
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"0 4 6 551\n"
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"2 5 7 385\n"
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"1 5 8 561\n"
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"5 3 9 484\n"
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"7 5 10 904\n"
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"3 6 11 47\n"
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"7 6 12 888\n"
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"3 0 13 747\n"
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"6 1 14 310\n",
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"@nodes\n"
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"label\n"
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"0\n"
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"1\n"
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"2\n"
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"3\n"
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"4\n"
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"5\n"
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"6\n"
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"7\n"
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"@edges\n"
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" label weight\n"
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"2 5 0 710\n"
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"0 5 1 241\n"
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"2 4 2 856\n"
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"2 6 3 762\n"
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"4 1 4 747\n"
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"6 1 5 962\n"
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"4 7 6 723\n"
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"1 7 7 661\n"
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"2 3 8 376\n"
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"1 0 9 416\n"
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"6 7 10 391\n",
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"@nodes\n"
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"label\n"
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"0\n"
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"1\n"
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"2\n"
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"3\n"
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"4\n"
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"5\n"
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"6\n"
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"7\n"
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"@edges\n"
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" label weight\n"
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"6 2 0 553\n"
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"0 7 1 653\n"
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"6 3 2 22\n"
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"4 7 3 846\n"
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"7 2 4 981\n"
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"7 6 5 250\n"
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"5 2 6 539\n",
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"@nodes\n"
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"label\n"
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"0\n"
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"@edges\n"
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" label weight\n"
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"0 0 0 100\n"
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};
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void checkMaxFractionalMatchingCompile()
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{
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typedef concepts::Graph Graph;
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typedef Graph::Node Node;
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typedef Graph::Edge Edge;
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Graph g;
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Node n;
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Edge e;
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MaxFractionalMatching<Graph> mat_test(g);
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const MaxFractionalMatching<Graph>&
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const_mat_test = mat_test;
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mat_test.init();
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mat_test.start();
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mat_test.start(true);
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mat_test.startPerfect();
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mat_test.startPerfect(true);
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mat_test.run();
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mat_test.run(true);
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mat_test.runPerfect();
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mat_test.runPerfect(true);
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const_mat_test.matchingSize();
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const_mat_test.matching(e);
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const_mat_test.matching(n);
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const MaxFractionalMatching<Graph>::MatchingMap& mmap =
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const_mat_test.matchingMap();
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e = mmap[n];
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const_mat_test.barrier(n);
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}
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void checkMaxWeightedFractionalMatchingCompile()
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{
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typedef concepts::Graph Graph;
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typedef Graph::Node Node;
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typedef Graph::Edge Edge;
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typedef Graph::EdgeMap<int> WeightMap;
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Graph g;
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Node n;
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Edge e;
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WeightMap w(g);
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MaxWeightedFractionalMatching<Graph> mat_test(g, w);
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const MaxWeightedFractionalMatching<Graph>&
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const_mat_test = mat_test;
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mat_test.init();
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mat_test.start();
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mat_test.run();
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const_mat_test.matchingWeight();
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const_mat_test.matchingSize();
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const_mat_test.matching(e);
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const_mat_test.matching(n);
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const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
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const_mat_test.matchingMap();
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e = mmap[n];
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const_mat_test.dualValue();
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const_mat_test.nodeValue(n);
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}
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void checkMaxWeightedPerfectFractionalMatchingCompile()
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{
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typedef concepts::Graph Graph;
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typedef Graph::Node Node;
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typedef Graph::Edge Edge;
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typedef Graph::EdgeMap<int> WeightMap;
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Graph g;
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Node n;
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Edge e;
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WeightMap w(g);
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MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
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const MaxWeightedPerfectFractionalMatching<Graph>&
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const_mat_test = mat_test;
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mat_test.init();
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mat_test.start();
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mat_test.run();
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const_mat_test.matchingWeight();
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const_mat_test.matching(e);
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const_mat_test.matching(n);
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const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
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const_mat_test.matchingMap();
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e = mmap[n];
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const_mat_test.dualValue();
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const_mat_test.nodeValue(n);
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}
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void checkFractionalMatching(const SmartGraph& graph,
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const MaxFractionalMatching<SmartGraph>& mfm,
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bool allow_loops = true) {
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int pv = 0;
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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int indeg = 0;
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for (InArcIt a(graph, n); a != INVALID; ++a) {
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if (mfm.matching(graph.source(a)) == a) {
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++indeg;
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}
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}
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if (mfm.matching(n) != INVALID) {
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check(indeg == 1, "Invalid matching");
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++pv;
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} else {
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check(indeg == 0, "Invalid matching");
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}
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}
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check(pv == mfm.matchingSize(), "Wrong matching size");
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for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
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(e == mfm.matching(graph.v(e)) ? 1 : 0) ==
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mfm.matching(e), "Invalid matching");
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}
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SmartGraph::NodeMap<bool> processed(graph, false);
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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if (processed[n]) continue;
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processed[n] = true;
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if (mfm.matching(n) == INVALID) continue;
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int num = 1;
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Node v = graph.target(mfm.matching(n));
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while (v != n) {
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processed[v] = true;
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++num;
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v = graph.target(mfm.matching(v));
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}
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check(num == 2 || num % 2 == 1, "Wrong cycle size");
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check(allow_loops || num != 1, "Wrong cycle size");
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}
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int anum = 0, bnum = 0;
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SmartGraph::NodeMap<bool> neighbours(graph, false);
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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if (!mfm.barrier(n)) continue;
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++anum;
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for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
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Node u = graph.source(a);
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if (!allow_loops && u == n) continue;
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if (!neighbours[u]) {
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neighbours[u] = true;
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++bnum;
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}
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}
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}
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check(anum - bnum + mfm.matchingSize() == countNodes(graph),
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"Wrong barrier");
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}
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void checkPerfectFractionalMatching(const SmartGraph& graph,
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const MaxFractionalMatching<SmartGraph>& mfm,
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bool perfect, bool allow_loops = true) {
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if (perfect) {
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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int indeg = 0;
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for (InArcIt a(graph, n); a != INVALID; ++a) {
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if (mfm.matching(graph.source(a)) == a) {
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++indeg;
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}
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}
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check(mfm.matching(n) != INVALID, "Invalid matching");
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check(indeg == 1, "Invalid matching");
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}
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for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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check((e == mfm.matching(graph.u(e)) ? 1 : 0) +
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(e == mfm.matching(graph.v(e)) ? 1 : 0) ==
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mfm.matching(e), "Invalid matching");
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}
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} else {
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int anum = 0, bnum = 0;
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SmartGraph::NodeMap<bool> neighbours(graph, false);
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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if (!mfm.barrier(n)) continue;
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++anum;
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for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
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Node u = graph.source(a);
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if (!allow_loops && u == n) continue;
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if (!neighbours[u]) {
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neighbours[u] = true;
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++bnum;
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}
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}
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}
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check(anum - bnum > 0, "Wrong barrier");
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}
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}
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void checkWeightedFractionalMatching(const SmartGraph& graph,
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const SmartGraph::EdgeMap<int>& weight,
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const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
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bool allow_loops = true) {
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for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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if (graph.u(e) == graph.v(e) && !allow_loops) continue;
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int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
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- weight[e] * mwfm.dualScale;
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check(rw >= 0, "Negative reduced weight");
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check(rw == 0 || !mwfm.matching(e),
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"Non-zero reduced weight on matching edge");
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}
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int pv = 0;
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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int indeg = 0;
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for (InArcIt a(graph, n); a != INVALID; ++a) {
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if (mwfm.matching(graph.source(a)) == a) {
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++indeg;
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}
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}
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check(indeg <= 1, "Invalid matching");
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if (mwfm.matching(n) != INVALID) {
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check(mwfm.nodeValue(n) >= 0, "Invalid node value");
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check(indeg == 1, "Invalid matching");
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pv += weight[mwfm.matching(n)];
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SmartGraph::Node o = graph.target(mwfm.matching(n));
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::lemon::ignore_unused_variable_warning(o);
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} else {
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check(mwfm.nodeValue(n) == 0, "Invalid matching");
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check(indeg == 0, "Invalid matching");
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}
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}
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for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
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check((e == mwfm.matching(graph.u(e)) ? 1 : 0) +
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(e == mwfm.matching(graph.v(e)) ? 1 : 0) ==
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mwfm.matching(e), "Invalid matching");
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}
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int dv = 0;
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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dv += mwfm.nodeValue(n);
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}
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check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
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SmartGraph::NodeMap<bool> processed(graph, false);
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for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
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if (processed[n]) continue;
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processed[n] = true;
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if (mwfm.matching(n) == INVALID) continue;
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int num = 1;
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Node v = graph.target(mwfm.matching(n));
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while (v != n) {
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processed[v] = true;
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++num;
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v = graph.target(mwfm.matching(v));
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}
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||
|
|
check(num == 2 || num % 2 == 1, "Wrong cycle size");
|
||
|
|
check(allow_loops || num != 1, "Wrong cycle size");
|
||
|
|
}
|
||
|
|
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
|
||
|
|
const SmartGraph::EdgeMap<int>& weight,
|
||
|
|
const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
|
||
|
|
bool allow_loops = true) {
|
||
|
|
for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
|
||
|
|
if (graph.u(e) == graph.v(e) && !allow_loops) continue;
|
||
|
|
int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
|
||
|
|
- weight[e] * mwpfm.dualScale;
|
||
|
|
|
||
|
|
check(rw >= 0, "Negative reduced weight");
|
||
|
|
check(rw == 0 || !mwpfm.matching(e),
|
||
|
|
"Non-zero reduced weight on matching edge");
|
||
|
|
}
|
||
|
|
|
||
|
|
int pv = 0;
|
||
|
|
for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
|
||
|
|
int indeg = 0;
|
||
|
|
for (InArcIt a(graph, n); a != INVALID; ++a) {
|
||
|
|
if (mwpfm.matching(graph.source(a)) == a) {
|
||
|
|
++indeg;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
|
||
|
|
check(indeg == 1, "Invalid perfect matching");
|
||
|
|
pv += weight[mwpfm.matching(n)];
|
||
|
|
SmartGraph::Node o = graph.target(mwpfm.matching(n));
|
||
|
|
::lemon::ignore_unused_variable_warning(o);
|
||
|
|
}
|
||
|
|
|
||
|
|
for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
|
||
|
|
check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) +
|
||
|
|
(e == mwpfm.matching(graph.v(e)) ? 1 : 0) ==
|
||
|
|
mwpfm.matching(e), "Invalid matching");
|
||
|
|
}
|
||
|
|
|
||
|
|
int dv = 0;
|
||
|
|
for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
|
||
|
|
dv += mwpfm.nodeValue(n);
|
||
|
|
}
|
||
|
|
|
||
|
|
check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
|
||
|
|
|
||
|
|
SmartGraph::NodeMap<bool> processed(graph, false);
|
||
|
|
for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
|
||
|
|
if (processed[n]) continue;
|
||
|
|
processed[n] = true;
|
||
|
|
if (mwpfm.matching(n) == INVALID) continue;
|
||
|
|
int num = 1;
|
||
|
|
Node v = graph.target(mwpfm.matching(n));
|
||
|
|
while (v != n) {
|
||
|
|
processed[v] = true;
|
||
|
|
++num;
|
||
|
|
v = graph.target(mwpfm.matching(v));
|
||
|
|
}
|
||
|
|
check(num == 2 || num % 2 == 1, "Wrong cycle size");
|
||
|
|
check(allow_loops || num != 1, "Wrong cycle size");
|
||
|
|
}
|
||
|
|
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
int main() {
|
||
|
|
|
||
|
|
for (int i = 0; i < lgfn; ++i) {
|
||
|
|
SmartGraph graph;
|
||
|
|
SmartGraph::EdgeMap<int> weight(graph);
|
||
|
|
|
||
|
|
istringstream lgfs(lgf[i]);
|
||
|
|
graphReader(graph, lgfs).
|
||
|
|
edgeMap("weight", weight).run();
|
||
|
|
|
||
|
|
bool perfect_with_loops;
|
||
|
|
{
|
||
|
|
MaxFractionalMatching<SmartGraph> mfm(graph, true);
|
||
|
|
mfm.run();
|
||
|
|
checkFractionalMatching(graph, mfm, true);
|
||
|
|
perfect_with_loops = mfm.matchingSize() == countNodes(graph);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool perfect_without_loops;
|
||
|
|
{
|
||
|
|
MaxFractionalMatching<SmartGraph> mfm(graph, false);
|
||
|
|
mfm.run();
|
||
|
|
checkFractionalMatching(graph, mfm, false);
|
||
|
|
perfect_without_loops = mfm.matchingSize() == countNodes(graph);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxFractionalMatching<SmartGraph> mfm(graph, true);
|
||
|
|
bool result = mfm.runPerfect();
|
||
|
|
checkPerfectFractionalMatching(graph, mfm, result, true);
|
||
|
|
check(result == perfect_with_loops, "Wrong perfect matching");
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxFractionalMatching<SmartGraph> mfm(graph, false);
|
||
|
|
bool result = mfm.runPerfect();
|
||
|
|
checkPerfectFractionalMatching(graph, mfm, result, false);
|
||
|
|
check(result == perfect_without_loops, "Wrong perfect matching");
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
|
||
|
|
mwfm.run();
|
||
|
|
checkWeightedFractionalMatching(graph, weight, mwfm, true);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
|
||
|
|
mwfm.run();
|
||
|
|
checkWeightedFractionalMatching(graph, weight, mwfm, false);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
|
||
|
|
true);
|
||
|
|
bool perfect = mwpfm.run();
|
||
|
|
check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
|
||
|
|
"Perfect matching found");
|
||
|
|
check(perfect == perfect_with_loops, "Wrong perfect matching");
|
||
|
|
|
||
|
|
if (perfect) {
|
||
|
|
checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
|
||
|
|
false);
|
||
|
|
bool perfect = mwpfm.run();
|
||
|
|
check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
|
||
|
|
"Perfect matching found");
|
||
|
|
check(perfect == perfect_without_loops, "Wrong perfect matching");
|
||
|
|
|
||
|
|
if (perfect) {
|
||
|
|
checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|