450 lines
11 KiB
C++
450 lines
11 KiB
C++
|
/* -*- mode: C++; indent-tabs-mode: nil; -*-
|
||
|
|
*
|
||
|
|
* This file is a part of LEMON, a generic C++ optimization library.
|
||
|
|
*
|
||
|
|
* Copyright (C) 2003-2013
|
||
|
|
* 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 <cstdlib>
|
||
|
|
|
||
|
|
#include <lemon/matching.h>
|
||
|
|
#include <lemon/smart_graph.h>
|
||
|
|
#include <lemon/concepts/graph.h>
|
||
|
|
#include <lemon/concepts/maps.h>
|
||
|
|
#include <lemon/lgf_reader.h>
|
||
|
|
#include <lemon/math.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 checkMaxMatchingCompile()
|
||
|
|
{
|
||
|
|
typedef concepts::Graph Graph;
|
||
|
|
typedef Graph::Node Node;
|
||
|
|
typedef Graph::Edge Edge;
|
||
|
|
typedef Graph::EdgeMap<bool> MatMap;
|
||
|
|
|
||
|
|
Graph g;
|
||
|
|
Node n;
|
||
|
|
Edge e;
|
||
|
|
MatMap mat(g);
|
||
|
|
|
||
|
|
MaxMatching<Graph> mat_test(g);
|
||
|
|
const MaxMatching<Graph>&
|
||
|
|
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<Graph>::MatchingMap& mmap =
|
||
|
|
const_mat_test.matchingMap();
|
||
|
|
e = mmap[n];
|
||
|
|
const_mat_test.mate(n);
|
||
|
|
|
||
|
|
MaxMatching<Graph>::Status stat =
|
||
|
|
const_mat_test.status(n);
|
||
|
|
::lemon::ignore_unused_variable_warning(stat);
|
||
|
|
const MaxMatching<Graph>::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<int> WeightMap;
|
||
|
|
|
||
|
|
Graph g;
|
||
|
|
Node n;
|
||
|
|
Edge e;
|
||
|
|
WeightMap w(g);
|
||
|
|
|
||
|
|
MaxWeightedMatching<Graph> mat_test(g, w);
|
||
|
|
const MaxWeightedMatching<Graph>&
|
||
|
|
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<Graph>::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<int> WeightMap;
|
||
|
|
|
||
|
|
Graph g;
|
||
|
|
Node n;
|
||
|
|
Edge e;
|
||
|
|
WeightMap w(g);
|
||
|
|
|
||
|
|
MaxWeightedPerfectMatching<Graph> mat_test(g, w);
|
||
|
|
const MaxWeightedPerfectMatching<Graph>&
|
||
|
|
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<Graph>::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<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.status(n) == MaxMatching<SmartGraph>::EVEN ||
|
||
|
|
mm.matching(n) != INVALID, "Wrong Gallai-Edmonds decomposition");
|
||
|
|
if (mm.status(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.status(graph.u(e)) != MaxMatching<SmartGraph>::EVEN ||
|
||
|
|
mm.status(graph.v(e)) != MaxMatching<SmartGraph>::MATCHED,
|
||
|
|
"Wrong Gallai-Edmonds decomposition");
|
||
|
|
|
||
|
|
check(mm.status(graph.v(e)) != MaxMatching<SmartGraph>::EVEN ||
|
||
|
|
mm.status(graph.u(e)) != MaxMatching<SmartGraph>::MATCHED,
|
||
|
|
"Wrong Gallai-Edmonds decomposition");
|
||
|
|
|
||
|
|
if (mm.status(graph.u(e)) != MaxMatching<SmartGraph>::ODD &&
|
||
|
|
mm.status(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.status(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();
|
||
|
|
|
||
|
|
bool perfect;
|
||
|
|
{
|
||
|
|
MaxMatching<SmartGraph> mm(graph);
|
||
|
|
mm.run();
|
||
|
|
checkMatching(graph, mm);
|
||
|
|
perfect = 2 * mm.matchingSize() == countNodes(graph);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedMatching<SmartGraph> mwm(graph, weight);
|
||
|
|
mwm.run();
|
||
|
|
checkWeightedMatching(graph, weight, mwm);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedMatching<SmartGraph> mwm(graph, weight);
|
||
|
|
mwm.init();
|
||
|
|
mwm.start();
|
||
|
|
checkWeightedMatching(graph, weight, mwm);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
|
||
|
|
bool result = mwpm.run();
|
||
|
|
|
||
|
|
check(result == perfect, "Perfect matching found");
|
||
|
|
if (perfect) {
|
||
|
|
checkWeightedPerfectMatching(graph, weight, mwpm);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
MaxWeightedPerfectMatching<SmartGraph> mwpm(graph, weight);
|
||
|
|
mwpm.init();
|
||
|
|
bool result = mwpm.start();
|
||
|
|
|
||
|
|
check(result == perfect, "Perfect matching found");
|
||
|
|
if (perfect) {
|
||
|
|
checkWeightedPerfectMatching(graph, weight, mwpm);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|