source: lemon-1.2/test/max_matching_test.cc @ 358:636fa2f39f10

/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2008
 * 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 <iostream>
#include <sstream>
#include <vector>
#include <queue>
#include <lemon/math.h>
#include <cstdlib>

#include <lemon/max_matching.h>
#include <lemon/smart_graph.h>
#include <lemon/lgf_reader.h>

#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 checkMatching(const SmartGraph& graph,
                   const MaxMatching<SmartGraph>& mm) {
  int num = 0;

  IntNodeMap comp_index(graph);
  UnionFind<IntNodeMap> comp(comp_index);

  int barrier_num = 0;

  for (NodeIt n(graph); n != INVALID; ++n) {
    check(mm.decomposition(n) == MaxMatching<SmartGraph>::EVEN ||
          mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
    if (mm.decomposition(n) == MaxMatching<SmartGraph>::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.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
          mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
          "Wrong Gallai-Edmonds decomposition");

    check(mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
          mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
          "Wrong Gallai-Edmonds decomposition");

    if (mm.decomposition(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
        mm.decomposition(graph.v(e)) != MaxMatching<SmartGraph>::ODD) {
      comp.join(graph.u(e), graph.v(e));
    }
  }

  std::set<int> comp_root;
  int odd_comp_num = 0;
  for (NodeIt n(graph); n != INVALID; ++n) {
    if (mm.decomposition(n) != MaxMatching<SmartGraph>::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<int>& weight,
                   const MaxWeightedMatching<SmartGraph>& 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<SmartGraph>::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<int>& weight,
                          const MaxWeightedPerfectMatching<SmartGraph>& 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<SmartGraph>::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<int> weight(graph);

    istringstream lgfs(lgf[i]);
    graphReader(graph, lgfs).
      edgeMap("weight", weight).run();

    MaxMatching<SmartGraph> mm(graph);
    mm.run();
    checkMatching(graph, mm);

    MaxWeightedMatching<SmartGraph> mwm(graph, weight);
    mwm.run();
    checkWeightedMatching(graph, weight, mwm);

    MaxWeightedPerfectMatching<SmartGraph> 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;
}