1.1 --- a/doc/groups.dox Sun Sep 20 21:38:24 2009 +0200
1.2 +++ b/doc/groups.dox Fri Sep 25 21:51:36 2009 +0200
1.3 @@ -349,7 +349,7 @@
1.4 also provide functions to query the minimum cut, which is the dual
1.5 problem of maximum flow.
1.6
1.7 -\ref Circulation is a preflow push-relabel algorithm implemented directly
1.8 +\ref Circulation is a preflow push-relabel algorithm implemented directly
1.9 for finding feasible circulations, which is a somewhat different problem,
1.10 but it is strongly related to maximum flow.
1.11 For more information, see \ref Circulation.
1.12 @@ -470,6 +470,13 @@
1.13 - \ref MaxWeightedPerfectMatching
1.14 Edmond's blossom shrinking algorithm for calculating maximum weighted
1.15 perfect matching in general graphs.
1.16 +- \ref MaxFractionalMatching Push-relabel algorithm for calculating
1.17 + maximum cardinality fractional matching in general graphs.
1.18 +- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
1.19 + maximum weighted fractional matching in general graphs.
1.20 +- \ref MaxWeightedPerfectFractionalMatching
1.21 + Augmenting path algorithm for calculating maximum weighted
1.22 + perfect fractional matching in general graphs.
1.23
1.24 \image html bipartite_matching.png
1.25 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
2.1 --- a/lemon/Makefile.am Sun Sep 20 21:38:24 2009 +0200
2.2 +++ b/lemon/Makefile.am Fri Sep 25 21:51:36 2009 +0200
2.3 @@ -81,6 +81,7 @@
2.4 lemon/euler.h \
2.5 lemon/fib_heap.h \
2.6 lemon/fourary_heap.h \
2.7 + lemon/fractional_matching.h \
2.8 lemon/full_graph.h \
2.9 lemon/glpk.h \
2.10 lemon/gomory_hu.h \
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/lemon/fractional_matching.h Fri Sep 25 21:51:36 2009 +0200
3.3 @@ -0,0 +1,2135 @@
3.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
3.5 + *
3.6 + * This file is a part of LEMON, a generic C++ optimization library.
3.7 + *
3.8 + * Copyright (C) 2003-2009
3.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
3.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
3.11 + *
3.12 + * Permission to use, modify and distribute this software is granted
3.13 + * provided that this copyright notice appears in all copies. For
3.14 + * precise terms see the accompanying LICENSE file.
3.15 + *
3.16 + * This software is provided "AS IS" with no warranty of any kind,
3.17 + * express or implied, and with no claim as to its suitability for any
3.18 + * purpose.
3.19 + *
3.20 + */
3.21 +
3.22 +#ifndef LEMON_FRACTIONAL_MATCHING_H
3.23 +#define LEMON_FRACTIONAL_MATCHING_H
3.24 +
3.25 +#include <vector>
3.26 +#include <queue>
3.27 +#include <set>
3.28 +#include <limits>
3.29 +
3.30 +#include <lemon/core.h>
3.31 +#include <lemon/unionfind.h>
3.32 +#include <lemon/bin_heap.h>
3.33 +#include <lemon/maps.h>
3.34 +#include <lemon/assert.h>
3.35 +#include <lemon/elevator.h>
3.36 +
3.37 +///\ingroup matching
3.38 +///\file
3.39 +///\brief Fractional matching algorithms in general graphs.
3.40 +
3.41 +namespace lemon {
3.42 +
3.43 + /// \brief Default traits class of MaxFractionalMatching class.
3.44 + ///
3.45 + /// Default traits class of MaxFractionalMatching class.
3.46 + /// \tparam GR Graph type.
3.47 + template <typename GR>
3.48 + struct MaxFractionalMatchingDefaultTraits {
3.49 +
3.50 + /// \brief The type of the graph the algorithm runs on.
3.51 + typedef GR Graph;
3.52 +
3.53 + /// \brief The type of the map that stores the matching.
3.54 + ///
3.55 + /// The type of the map that stores the matching arcs.
3.56 + /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
3.57 + typedef typename Graph::template NodeMap<typename GR::Arc> MatchingMap;
3.58 +
3.59 + /// \brief Instantiates a MatchingMap.
3.60 + ///
3.61 + /// This function instantiates a \ref MatchingMap.
3.62 + /// \param graph The graph for which we would like to define
3.63 + /// the matching map.
3.64 + static MatchingMap* createMatchingMap(const Graph& graph) {
3.65 + return new MatchingMap(graph);
3.66 + }
3.67 +
3.68 + /// \brief The elevator type used by MaxFractionalMatching algorithm.
3.69 + ///
3.70 + /// The elevator type used by MaxFractionalMatching algorithm.
3.71 + ///
3.72 + /// \sa Elevator
3.73 + /// \sa LinkedElevator
3.74 + typedef LinkedElevator<Graph, typename Graph::Node> Elevator;
3.75 +
3.76 + /// \brief Instantiates an Elevator.
3.77 + ///
3.78 + /// This function instantiates an \ref Elevator.
3.79 + /// \param graph The graph for which we would like to define
3.80 + /// the elevator.
3.81 + /// \param max_level The maximum level of the elevator.
3.82 + static Elevator* createElevator(const Graph& graph, int max_level) {
3.83 + return new Elevator(graph, max_level);
3.84 + }
3.85 + };
3.86 +
3.87 + /// \ingroup matching
3.88 + ///
3.89 + /// \brief Max cardinality fractional matching
3.90 + ///
3.91 + /// This class provides an implementation of fractional matching
3.92 + /// algorithm based on push-relabel principle.
3.93 + ///
3.94 + /// The maximum cardinality fractional matching is a relaxation of the
3.95 + /// maximum cardinality matching problem where the odd set constraints
3.96 + /// are omitted.
3.97 + /// It can be formulated with the following linear program.
3.98 + /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
3.99 + /// \f[x_e \ge 0\quad \forall e\in E\f]
3.100 + /// \f[\max \sum_{e\in E}x_e\f]
3.101 + /// where \f$\delta(X)\f$ is the set of edges incident to a node in
3.102 + /// \f$X\f$. The result can be represented as the union of a
3.103 + /// matching with one value edges and a set of odd length cycles
3.104 + /// with half value edges.
3.105 + ///
3.106 + /// The algorithm calculates an optimal fractional matching and a
3.107 + /// barrier. The number of adjacents of any node set minus the size
3.108 + /// of node set is a lower bound on the uncovered nodes in the
3.109 + /// graph. For maximum matching a barrier is computed which
3.110 + /// maximizes this difference.
3.111 + ///
3.112 + /// The algorithm can be executed with the run() function. After it
3.113 + /// the matching (the primal solution) and the barrier (the dual
3.114 + /// solution) can be obtained using the query functions.
3.115 + ///
3.116 + /// The primal solution is multiplied by
3.117 + /// \ref MaxWeightedMatching::primalScale "2".
3.118 + ///
3.119 + /// \tparam GR The undirected graph type the algorithm runs on.
3.120 +#ifdef DOXYGEN
3.121 + template <typename GR, typename TR>
3.122 +#else
3.123 + template <typename GR,
3.124 + typename TR = MaxFractionalMatchingDefaultTraits<GR> >
3.125 +#endif
3.126 + class MaxFractionalMatching {
3.127 + public:
3.128 +
3.129 + /// \brief The \ref MaxFractionalMatchingDefaultTraits "traits
3.130 + /// class" of the algorithm.
3.131 + typedef TR Traits;
3.132 + /// The type of the graph the algorithm runs on.
3.133 + typedef typename TR::Graph Graph;
3.134 + /// The type of the matching map.
3.135 + typedef typename TR::MatchingMap MatchingMap;
3.136 + /// The type of the elevator.
3.137 + typedef typename TR::Elevator Elevator;
3.138 +
3.139 + /// \brief Scaling factor for primal solution
3.140 + ///
3.141 + /// Scaling factor for primal solution.
3.142 + static const int primalScale = 2;
3.143 +
3.144 + private:
3.145 +
3.146 + const Graph &_graph;
3.147 + int _node_num;
3.148 + bool _allow_loops;
3.149 + int _empty_level;
3.150 +
3.151 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
3.152 +
3.153 + bool _local_matching;
3.154 + MatchingMap *_matching;
3.155 +
3.156 + bool _local_level;
3.157 + Elevator *_level;
3.158 +
3.159 + typedef typename Graph::template NodeMap<int> InDegMap;
3.160 + InDegMap *_indeg;
3.161 +
3.162 + void createStructures() {
3.163 + _node_num = countNodes(_graph);
3.164 +
3.165 + if (!_matching) {
3.166 + _local_matching = true;
3.167 + _matching = Traits::createMatchingMap(_graph);
3.168 + }
3.169 + if (!_level) {
3.170 + _local_level = true;
3.171 + _level = Traits::createElevator(_graph, _node_num);
3.172 + }
3.173 + if (!_indeg) {
3.174 + _indeg = new InDegMap(_graph);
3.175 + }
3.176 + }
3.177 +
3.178 + void destroyStructures() {
3.179 + if (_local_matching) {
3.180 + delete _matching;
3.181 + }
3.182 + if (_local_level) {
3.183 + delete _level;
3.184 + }
3.185 + if (_indeg) {
3.186 + delete _indeg;
3.187 + }
3.188 + }
3.189 +
3.190 + void postprocessing() {
3.191 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.192 + if ((*_indeg)[n] != 0) continue;
3.193 + _indeg->set(n, -1);
3.194 + Node u = n;
3.195 + while ((*_matching)[u] != INVALID) {
3.196 + Node v = _graph.target((*_matching)[u]);
3.197 + _indeg->set(v, -1);
3.198 + Arc a = _graph.oppositeArc((*_matching)[u]);
3.199 + u = _graph.target((*_matching)[v]);
3.200 + _indeg->set(u, -1);
3.201 + _matching->set(v, a);
3.202 + }
3.203 + }
3.204 +
3.205 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.206 + if ((*_indeg)[n] != 1) continue;
3.207 + _indeg->set(n, -1);
3.208 +
3.209 + int num = 1;
3.210 + Node u = _graph.target((*_matching)[n]);
3.211 + while (u != n) {
3.212 + _indeg->set(u, -1);
3.213 + u = _graph.target((*_matching)[u]);
3.214 + ++num;
3.215 + }
3.216 + if (num % 2 == 0 && num > 2) {
3.217 + Arc prev = _graph.oppositeArc((*_matching)[n]);
3.218 + Node v = _graph.target((*_matching)[n]);
3.219 + u = _graph.target((*_matching)[v]);
3.220 + _matching->set(v, prev);
3.221 + while (u != n) {
3.222 + prev = _graph.oppositeArc((*_matching)[u]);
3.223 + v = _graph.target((*_matching)[u]);
3.224 + u = _graph.target((*_matching)[v]);
3.225 + _matching->set(v, prev);
3.226 + }
3.227 + }
3.228 + }
3.229 + }
3.230 +
3.231 + public:
3.232 +
3.233 + typedef MaxFractionalMatching Create;
3.234 +
3.235 + ///\name Named Template Parameters
3.236 +
3.237 + ///@{
3.238 +
3.239 + template <typename T>
3.240 + struct SetMatchingMapTraits : public Traits {
3.241 + typedef T MatchingMap;
3.242 + static MatchingMap *createMatchingMap(const Graph&) {
3.243 + LEMON_ASSERT(false, "MatchingMap is not initialized");
3.244 + return 0; // ignore warnings
3.245 + }
3.246 + };
3.247 +
3.248 + /// \brief \ref named-templ-param "Named parameter" for setting
3.249 + /// MatchingMap type
3.250 + ///
3.251 + /// \ref named-templ-param "Named parameter" for setting MatchingMap
3.252 + /// type.
3.253 + template <typename T>
3.254 + struct SetMatchingMap
3.255 + : public MaxFractionalMatching<Graph, SetMatchingMapTraits<T> > {
3.256 + typedef MaxFractionalMatching<Graph, SetMatchingMapTraits<T> > Create;
3.257 + };
3.258 +
3.259 + template <typename T>
3.260 + struct SetElevatorTraits : public Traits {
3.261 + typedef T Elevator;
3.262 + static Elevator *createElevator(const Graph&, int) {
3.263 + LEMON_ASSERT(false, "Elevator is not initialized");
3.264 + return 0; // ignore warnings
3.265 + }
3.266 + };
3.267 +
3.268 + /// \brief \ref named-templ-param "Named parameter" for setting
3.269 + /// Elevator type
3.270 + ///
3.271 + /// \ref named-templ-param "Named parameter" for setting Elevator
3.272 + /// type. If this named parameter is used, then an external
3.273 + /// elevator object must be passed to the algorithm using the
3.274 + /// \ref elevator(Elevator&) "elevator()" function before calling
3.275 + /// \ref run() or \ref init().
3.276 + /// \sa SetStandardElevator
3.277 + template <typename T>
3.278 + struct SetElevator
3.279 + : public MaxFractionalMatching<Graph, SetElevatorTraits<T> > {
3.280 + typedef MaxFractionalMatching<Graph, SetElevatorTraits<T> > Create;
3.281 + };
3.282 +
3.283 + template <typename T>
3.284 + struct SetStandardElevatorTraits : public Traits {
3.285 + typedef T Elevator;
3.286 + static Elevator *createElevator(const Graph& graph, int max_level) {
3.287 + return new Elevator(graph, max_level);
3.288 + }
3.289 + };
3.290 +
3.291 + /// \brief \ref named-templ-param "Named parameter" for setting
3.292 + /// Elevator type with automatic allocation
3.293 + ///
3.294 + /// \ref named-templ-param "Named parameter" for setting Elevator
3.295 + /// type with automatic allocation.
3.296 + /// The Elevator should have standard constructor interface to be
3.297 + /// able to automatically created by the algorithm (i.e. the
3.298 + /// graph and the maximum level should be passed to it).
3.299 + /// However an external elevator object could also be passed to the
3.300 + /// algorithm with the \ref elevator(Elevator&) "elevator()" function
3.301 + /// before calling \ref run() or \ref init().
3.302 + /// \sa SetElevator
3.303 + template <typename T>
3.304 + struct SetStandardElevator
3.305 + : public MaxFractionalMatching<Graph, SetStandardElevatorTraits<T> > {
3.306 + typedef MaxFractionalMatching<Graph,
3.307 + SetStandardElevatorTraits<T> > Create;
3.308 + };
3.309 +
3.310 + /// @}
3.311 +
3.312 + protected:
3.313 +
3.314 + MaxFractionalMatching() {}
3.315 +
3.316 + public:
3.317 +
3.318 + /// \brief Constructor
3.319 + ///
3.320 + /// Constructor.
3.321 + ///
3.322 + MaxFractionalMatching(const Graph &graph, bool allow_loops = true)
3.323 + : _graph(graph), _allow_loops(allow_loops),
3.324 + _local_matching(false), _matching(0),
3.325 + _local_level(false), _level(0), _indeg(0)
3.326 + {}
3.327 +
3.328 + ~MaxFractionalMatching() {
3.329 + destroyStructures();
3.330 + }
3.331 +
3.332 + /// \brief Sets the matching map.
3.333 + ///
3.334 + /// Sets the matching map.
3.335 + /// If you don't use this function before calling \ref run() or
3.336 + /// \ref init(), an instance will be allocated automatically.
3.337 + /// The destructor deallocates this automatically allocated map,
3.338 + /// of course.
3.339 + /// \return <tt>(*this)</tt>
3.340 + MaxFractionalMatching& matchingMap(MatchingMap& map) {
3.341 + if (_local_matching) {
3.342 + delete _matching;
3.343 + _local_matching = false;
3.344 + }
3.345 + _matching = ↦
3.346 + return *this;
3.347 + }
3.348 +
3.349 + /// \brief Sets the elevator used by algorithm.
3.350 + ///
3.351 + /// Sets the elevator used by algorithm.
3.352 + /// If you don't use this function before calling \ref run() or
3.353 + /// \ref init(), an instance will be allocated automatically.
3.354 + /// The destructor deallocates this automatically allocated elevator,
3.355 + /// of course.
3.356 + /// \return <tt>(*this)</tt>
3.357 + MaxFractionalMatching& elevator(Elevator& elevator) {
3.358 + if (_local_level) {
3.359 + delete _level;
3.360 + _local_level = false;
3.361 + }
3.362 + _level = &elevator;
3.363 + return *this;
3.364 + }
3.365 +
3.366 + /// \brief Returns a const reference to the elevator.
3.367 + ///
3.368 + /// Returns a const reference to the elevator.
3.369 + ///
3.370 + /// \pre Either \ref run() or \ref init() must be called before
3.371 + /// using this function.
3.372 + const Elevator& elevator() const {
3.373 + return *_level;
3.374 + }
3.375 +
3.376 + /// \name Execution control
3.377 + /// The simplest way to execute the algorithm is to use one of the
3.378 + /// member functions called \c run(). \n
3.379 + /// If you need more control on the execution, first
3.380 + /// you must call \ref init() and then one variant of the start()
3.381 + /// member.
3.382 +
3.383 + /// @{
3.384 +
3.385 + /// \brief Initializes the internal data structures.
3.386 + ///
3.387 + /// Initializes the internal data structures and sets the initial
3.388 + /// matching.
3.389 + void init() {
3.390 + createStructures();
3.391 +
3.392 + _level->initStart();
3.393 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.394 + _indeg->set(n, 0);
3.395 + _matching->set(n, INVALID);
3.396 + _level->initAddItem(n);
3.397 + }
3.398 + _level->initFinish();
3.399 +
3.400 + _empty_level = _node_num;
3.401 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.402 + for (OutArcIt a(_graph, n); a != INVALID; ++a) {
3.403 + if (_graph.target(a) == n && !_allow_loops) continue;
3.404 + _matching->set(n, a);
3.405 + Node v = _graph.target((*_matching)[n]);
3.406 + _indeg->set(v, (*_indeg)[v] + 1);
3.407 + break;
3.408 + }
3.409 + }
3.410 +
3.411 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.412 + if ((*_indeg)[n] == 0) {
3.413 + _level->activate(n);
3.414 + }
3.415 + }
3.416 + }
3.417 +
3.418 + /// \brief Starts the algorithm and computes a fractional matching
3.419 + ///
3.420 + /// The algorithm computes a maximum fractional matching.
3.421 + ///
3.422 + /// \param postprocess The algorithm computes first a matching
3.423 + /// which is a union of a matching with one value edges, cycles
3.424 + /// with half value edges and even length paths with half value
3.425 + /// edges. If the parameter is true, then after the push-relabel
3.426 + /// algorithm it postprocesses the matching to contain only
3.427 + /// matching edges and half value odd cycles.
3.428 + void start(bool postprocess = true) {
3.429 + Node n;
3.430 + while ((n = _level->highestActive()) != INVALID) {
3.431 + int level = _level->highestActiveLevel();
3.432 + int new_level = _level->maxLevel();
3.433 + for (InArcIt a(_graph, n); a != INVALID; ++a) {
3.434 + Node u = _graph.source(a);
3.435 + if (n == u && !_allow_loops) continue;
3.436 + Node v = _graph.target((*_matching)[u]);
3.437 + if ((*_level)[v] < level) {
3.438 + _indeg->set(v, (*_indeg)[v] - 1);
3.439 + if ((*_indeg)[v] == 0) {
3.440 + _level->activate(v);
3.441 + }
3.442 + _matching->set(u, a);
3.443 + _indeg->set(n, (*_indeg)[n] + 1);
3.444 + _level->deactivate(n);
3.445 + goto no_more_push;
3.446 + } else if (new_level > (*_level)[v]) {
3.447 + new_level = (*_level)[v];
3.448 + }
3.449 + }
3.450 +
3.451 + if (new_level + 1 < _level->maxLevel()) {
3.452 + _level->liftHighestActive(new_level + 1);
3.453 + } else {
3.454 + _level->liftHighestActiveToTop();
3.455 + }
3.456 + if (_level->emptyLevel(level)) {
3.457 + _level->liftToTop(level);
3.458 + }
3.459 + no_more_push:
3.460 + ;
3.461 + }
3.462 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.463 + if ((*_matching)[n] == INVALID) continue;
3.464 + Node u = _graph.target((*_matching)[n]);
3.465 + if ((*_indeg)[u] > 1) {
3.466 + _indeg->set(u, (*_indeg)[u] - 1);
3.467 + _matching->set(n, INVALID);
3.468 + }
3.469 + }
3.470 + if (postprocess) {
3.471 + postprocessing();
3.472 + }
3.473 + }
3.474 +
3.475 + /// \brief Starts the algorithm and computes a perfect fractional
3.476 + /// matching
3.477 + ///
3.478 + /// The algorithm computes a perfect fractional matching. If it
3.479 + /// does not exists, then the algorithm returns false and the
3.480 + /// matching is undefined and the barrier.
3.481 + ///
3.482 + /// \param postprocess The algorithm computes first a matching
3.483 + /// which is a union of a matching with one value edges, cycles
3.484 + /// with half value edges and even length paths with half value
3.485 + /// edges. If the parameter is true, then after the push-relabel
3.486 + /// algorithm it postprocesses the matching to contain only
3.487 + /// matching edges and half value odd cycles.
3.488 + bool startPerfect(bool postprocess = true) {
3.489 + Node n;
3.490 + while ((n = _level->highestActive()) != INVALID) {
3.491 + int level = _level->highestActiveLevel();
3.492 + int new_level = _level->maxLevel();
3.493 + for (InArcIt a(_graph, n); a != INVALID; ++a) {
3.494 + Node u = _graph.source(a);
3.495 + if (n == u && !_allow_loops) continue;
3.496 + Node v = _graph.target((*_matching)[u]);
3.497 + if ((*_level)[v] < level) {
3.498 + _indeg->set(v, (*_indeg)[v] - 1);
3.499 + if ((*_indeg)[v] == 0) {
3.500 + _level->activate(v);
3.501 + }
3.502 + _matching->set(u, a);
3.503 + _indeg->set(n, (*_indeg)[n] + 1);
3.504 + _level->deactivate(n);
3.505 + goto no_more_push;
3.506 + } else if (new_level > (*_level)[v]) {
3.507 + new_level = (*_level)[v];
3.508 + }
3.509 + }
3.510 +
3.511 + if (new_level + 1 < _level->maxLevel()) {
3.512 + _level->liftHighestActive(new_level + 1);
3.513 + } else {
3.514 + _level->liftHighestActiveToTop();
3.515 + _empty_level = _level->maxLevel() - 1;
3.516 + return false;
3.517 + }
3.518 + if (_level->emptyLevel(level)) {
3.519 + _level->liftToTop(level);
3.520 + _empty_level = level;
3.521 + return false;
3.522 + }
3.523 + no_more_push:
3.524 + ;
3.525 + }
3.526 + if (postprocess) {
3.527 + postprocessing();
3.528 + }
3.529 + return true;
3.530 + }
3.531 +
3.532 + /// \brief Runs the algorithm
3.533 + ///
3.534 + /// Just a shortcut for the next code:
3.535 + ///\code
3.536 + /// init();
3.537 + /// start();
3.538 + ///\endcode
3.539 + void run(bool postprocess = true) {
3.540 + init();
3.541 + start(postprocess);
3.542 + }
3.543 +
3.544 + /// \brief Runs the algorithm to find a perfect fractional matching
3.545 + ///
3.546 + /// Just a shortcut for the next code:
3.547 + ///\code
3.548 + /// init();
3.549 + /// startPerfect();
3.550 + ///\endcode
3.551 + bool runPerfect(bool postprocess = true) {
3.552 + init();
3.553 + return startPerfect(postprocess);
3.554 + }
3.555 +
3.556 + ///@}
3.557 +
3.558 + /// \name Query Functions
3.559 + /// The result of the %Matching algorithm can be obtained using these
3.560 + /// functions.\n
3.561 + /// Before the use of these functions,
3.562 + /// either run() or start() must be called.
3.563 + ///@{
3.564 +
3.565 +
3.566 + /// \brief Return the number of covered nodes in the matching.
3.567 + ///
3.568 + /// This function returns the number of covered nodes in the matching.
3.569 + ///
3.570 + /// \pre Either run() or start() must be called before using this function.
3.571 + int matchingSize() const {
3.572 + int num = 0;
3.573 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.574 + if ((*_matching)[n] != INVALID) {
3.575 + ++num;
3.576 + }
3.577 + }
3.578 + return num;
3.579 + }
3.580 +
3.581 + /// \brief Returns a const reference to the matching map.
3.582 + ///
3.583 + /// Returns a const reference to the node map storing the found
3.584 + /// fractional matching. This method can be called after
3.585 + /// running the algorithm.
3.586 + ///
3.587 + /// \pre Either \ref run() or \ref init() must be called before
3.588 + /// using this function.
3.589 + const MatchingMap& matchingMap() const {
3.590 + return *_matching;
3.591 + }
3.592 +
3.593 + /// \brief Return \c true if the given edge is in the matching.
3.594 + ///
3.595 + /// This function returns \c true if the given edge is in the
3.596 + /// found matching. The result is scaled by \ref primalScale
3.597 + /// "primal scale".
3.598 + ///
3.599 + /// \pre Either run() or start() must be called before using this function.
3.600 + int matching(const Edge& edge) const {
3.601 + return (edge == (*_matching)[_graph.u(edge)] ? 1 : 0) +
3.602 + (edge == (*_matching)[_graph.v(edge)] ? 1 : 0);
3.603 + }
3.604 +
3.605 + /// \brief Return the fractional matching arc (or edge) incident
3.606 + /// to the given node.
3.607 + ///
3.608 + /// This function returns one of the fractional matching arc (or
3.609 + /// edge) incident to the given node in the found matching or \c
3.610 + /// INVALID if the node is not covered by the matching or if the
3.611 + /// node is on an odd length cycle then it is the successor edge
3.612 + /// on the cycle.
3.613 + ///
3.614 + /// \pre Either run() or start() must be called before using this function.
3.615 + Arc matching(const Node& node) const {
3.616 + return (*_matching)[node];
3.617 + }
3.618 +
3.619 + /// \brief Returns true if the node is in the barrier
3.620 + ///
3.621 + /// The barrier is a subset of the nodes. If the nodes in the
3.622 + /// barrier have less adjacent nodes than the size of the barrier,
3.623 + /// then at least as much nodes cannot be covered as the
3.624 + /// difference of the two subsets.
3.625 + bool barrier(const Node& node) const {
3.626 + return (*_level)[node] >= _empty_level;
3.627 + }
3.628 +
3.629 + /// @}
3.630 +
3.631 + };
3.632 +
3.633 + /// \ingroup matching
3.634 + ///
3.635 + /// \brief Weighted fractional matching in general graphs
3.636 + ///
3.637 + /// This class provides an efficient implementation of fractional
3.638 + /// matching algorithm. The implementation is based on extensive use
3.639 + /// of priority queues and provides \f$O(nm\log n)\f$ time
3.640 + /// complexity.
3.641 + ///
3.642 + /// The maximum weighted fractional matching is a relaxation of the
3.643 + /// maximum weighted matching problem where the odd set constraints
3.644 + /// are omitted.
3.645 + /// It can be formulated with the following linear program.
3.646 + /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
3.647 + /// \f[x_e \ge 0\quad \forall e\in E\f]
3.648 + /// \f[\max \sum_{e\in E}x_ew_e\f]
3.649 + /// where \f$\delta(X)\f$ is the set of edges incident to a node in
3.650 + /// \f$X\f$. The result must be the union of a matching with one
3.651 + /// value edges and a set of odd length cycles with half value edges.
3.652 + ///
3.653 + /// The algorithm calculates an optimal fractional matching and a
3.654 + /// proof of the optimality. The solution of the dual problem can be
3.655 + /// used to check the result of the algorithm. The dual linear
3.656 + /// problem is the following.
3.657 + /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f]
3.658 + /// \f[y_u \ge 0 \quad \forall u \in V\f]
3.659 + /// \f[\min \sum_{u \in V}y_u \f] ///
3.660 + ///
3.661 + /// The algorithm can be executed with the run() function.
3.662 + /// After it the matching (the primal solution) and the dual solution
3.663 + /// can be obtained using the query functions.
3.664 + ///
3.665 + /// If the value type is integer, then the primal and the dual
3.666 + /// solutions are multiplied by
3.667 + /// \ref MaxWeightedMatching::primalScale "2" and
3.668 + /// \ref MaxWeightedMatching::dualScale "4" respectively.
3.669 + ///
3.670 + /// \tparam GR The undirected graph type the algorithm runs on.
3.671 + /// \tparam WM The type edge weight map. The default type is
3.672 + /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
3.673 +#ifdef DOXYGEN
3.674 + template <typename GR, typename WM>
3.675 +#else
3.676 + template <typename GR,
3.677 + typename WM = typename GR::template EdgeMap<int> >
3.678 +#endif
3.679 + class MaxWeightedFractionalMatching {
3.680 + public:
3.681 +
3.682 + /// The graph type of the algorithm
3.683 + typedef GR Graph;
3.684 + /// The type of the edge weight map
3.685 + typedef WM WeightMap;
3.686 + /// The value type of the edge weights
3.687 + typedef typename WeightMap::Value Value;
3.688 +
3.689 + /// The type of the matching map
3.690 + typedef typename Graph::template NodeMap<typename Graph::Arc>
3.691 + MatchingMap;
3.692 +
3.693 + /// \brief Scaling factor for primal solution
3.694 + ///
3.695 + /// Scaling factor for primal solution. It is equal to 2 or 1
3.696 + /// according to the value type.
3.697 + static const int primalScale =
3.698 + std::numeric_limits<Value>::is_integer ? 2 : 1;
3.699 +
3.700 + /// \brief Scaling factor for dual solution
3.701 + ///
3.702 + /// Scaling factor for dual solution. It is equal to 4 or 1
3.703 + /// according to the value type.
3.704 + static const int dualScale =
3.705 + std::numeric_limits<Value>::is_integer ? 4 : 1;
3.706 +
3.707 + private:
3.708 +
3.709 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
3.710 +
3.711 + typedef typename Graph::template NodeMap<Value> NodePotential;
3.712 +
3.713 + const Graph& _graph;
3.714 + const WeightMap& _weight;
3.715 +
3.716 + MatchingMap* _matching;
3.717 + NodePotential* _node_potential;
3.718 +
3.719 + int _node_num;
3.720 + bool _allow_loops;
3.721 +
3.722 + enum Status {
3.723 + EVEN = -1, MATCHED = 0, ODD = 1
3.724 + };
3.725 +
3.726 + typedef typename Graph::template NodeMap<Status> StatusMap;
3.727 + StatusMap* _status;
3.728 +
3.729 + typedef typename Graph::template NodeMap<Arc> PredMap;
3.730 + PredMap* _pred;
3.731 +
3.732 + typedef ExtendFindEnum<IntNodeMap> TreeSet;
3.733 +
3.734 + IntNodeMap *_tree_set_index;
3.735 + TreeSet *_tree_set;
3.736 +
3.737 + IntNodeMap *_delta1_index;
3.738 + BinHeap<Value, IntNodeMap> *_delta1;
3.739 +
3.740 + IntNodeMap *_delta2_index;
3.741 + BinHeap<Value, IntNodeMap> *_delta2;
3.742 +
3.743 + IntEdgeMap *_delta3_index;
3.744 + BinHeap<Value, IntEdgeMap> *_delta3;
3.745 +
3.746 + Value _delta_sum;
3.747 +
3.748 + void createStructures() {
3.749 + _node_num = countNodes(_graph);
3.750 +
3.751 + if (!_matching) {
3.752 + _matching = new MatchingMap(_graph);
3.753 + }
3.754 + if (!_node_potential) {
3.755 + _node_potential = new NodePotential(_graph);
3.756 + }
3.757 + if (!_status) {
3.758 + _status = new StatusMap(_graph);
3.759 + }
3.760 + if (!_pred) {
3.761 + _pred = new PredMap(_graph);
3.762 + }
3.763 + if (!_tree_set) {
3.764 + _tree_set_index = new IntNodeMap(_graph);
3.765 + _tree_set = new TreeSet(*_tree_set_index);
3.766 + }
3.767 + if (!_delta1) {
3.768 + _delta1_index = new IntNodeMap(_graph);
3.769 + _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
3.770 + }
3.771 + if (!_delta2) {
3.772 + _delta2_index = new IntNodeMap(_graph);
3.773 + _delta2 = new BinHeap<Value, IntNodeMap>(*_delta2_index);
3.774 + }
3.775 + if (!_delta3) {
3.776 + _delta3_index = new IntEdgeMap(_graph);
3.777 + _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
3.778 + }
3.779 + }
3.780 +
3.781 + void destroyStructures() {
3.782 + if (_matching) {
3.783 + delete _matching;
3.784 + }
3.785 + if (_node_potential) {
3.786 + delete _node_potential;
3.787 + }
3.788 + if (_status) {
3.789 + delete _status;
3.790 + }
3.791 + if (_pred) {
3.792 + delete _pred;
3.793 + }
3.794 + if (_tree_set) {
3.795 + delete _tree_set_index;
3.796 + delete _tree_set;
3.797 + }
3.798 + if (_delta1) {
3.799 + delete _delta1_index;
3.800 + delete _delta1;
3.801 + }
3.802 + if (_delta2) {
3.803 + delete _delta2_index;
3.804 + delete _delta2;
3.805 + }
3.806 + if (_delta3) {
3.807 + delete _delta3_index;
3.808 + delete _delta3;
3.809 + }
3.810 + }
3.811 +
3.812 + void matchedToEven(Node node, int tree) {
3.813 + _tree_set->insert(node, tree);
3.814 + _node_potential->set(node, (*_node_potential)[node] + _delta_sum);
3.815 + _delta1->push(node, (*_node_potential)[node]);
3.816 +
3.817 + if (_delta2->state(node) == _delta2->IN_HEAP) {
3.818 + _delta2->erase(node);
3.819 + }
3.820 +
3.821 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.822 + Node v = _graph.source(a);
3.823 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.824 + dualScale * _weight[a];
3.825 + if (node == v) {
3.826 + if (_allow_loops && _graph.direction(a)) {
3.827 + _delta3->push(a, rw / 2);
3.828 + }
3.829 + } else if ((*_status)[v] == EVEN) {
3.830 + _delta3->push(a, rw / 2);
3.831 + } else if ((*_status)[v] == MATCHED) {
3.832 + if (_delta2->state(v) != _delta2->IN_HEAP) {
3.833 + _pred->set(v, a);
3.834 + _delta2->push(v, rw);
3.835 + } else if ((*_delta2)[v] > rw) {
3.836 + _pred->set(v, a);
3.837 + _delta2->decrease(v, rw);
3.838 + }
3.839 + }
3.840 + }
3.841 + }
3.842 +
3.843 + void matchedToOdd(Node node, int tree) {
3.844 + _tree_set->insert(node, tree);
3.845 + _node_potential->set(node, (*_node_potential)[node] - _delta_sum);
3.846 +
3.847 + if (_delta2->state(node) == _delta2->IN_HEAP) {
3.848 + _delta2->erase(node);
3.849 + }
3.850 + }
3.851 +
3.852 + void evenToMatched(Node node, int tree) {
3.853 + _delta1->erase(node);
3.854 + _node_potential->set(node, (*_node_potential)[node] - _delta_sum);
3.855 + Arc min = INVALID;
3.856 + Value minrw = std::numeric_limits<Value>::max();
3.857 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.858 + Node v = _graph.source(a);
3.859 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.860 + dualScale * _weight[a];
3.861 +
3.862 + if (node == v) {
3.863 + if (_allow_loops && _graph.direction(a)) {
3.864 + _delta3->erase(a);
3.865 + }
3.866 + } else if ((*_status)[v] == EVEN) {
3.867 + _delta3->erase(a);
3.868 + if (minrw > rw) {
3.869 + min = _graph.oppositeArc(a);
3.870 + minrw = rw;
3.871 + }
3.872 + } else if ((*_status)[v] == MATCHED) {
3.873 + if ((*_pred)[v] == a) {
3.874 + Arc mina = INVALID;
3.875 + Value minrwa = std::numeric_limits<Value>::max();
3.876 + for (OutArcIt aa(_graph, v); aa != INVALID; ++aa) {
3.877 + Node va = _graph.target(aa);
3.878 + if ((*_status)[va] != EVEN ||
3.879 + _tree_set->find(va) == tree) continue;
3.880 + Value rwa = (*_node_potential)[v] + (*_node_potential)[va] -
3.881 + dualScale * _weight[aa];
3.882 + if (minrwa > rwa) {
3.883 + minrwa = rwa;
3.884 + mina = aa;
3.885 + }
3.886 + }
3.887 + if (mina != INVALID) {
3.888 + _pred->set(v, mina);
3.889 + _delta2->increase(v, minrwa);
3.890 + } else {
3.891 + _pred->set(v, INVALID);
3.892 + _delta2->erase(v);
3.893 + }
3.894 + }
3.895 + }
3.896 + }
3.897 + if (min != INVALID) {
3.898 + _pred->set(node, min);
3.899 + _delta2->push(node, minrw);
3.900 + } else {
3.901 + _pred->set(node, INVALID);
3.902 + }
3.903 + }
3.904 +
3.905 + void oddToMatched(Node node) {
3.906 + _node_potential->set(node, (*_node_potential)[node] + _delta_sum);
3.907 + Arc min = INVALID;
3.908 + Value minrw = std::numeric_limits<Value>::max();
3.909 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.910 + Node v = _graph.source(a);
3.911 + if ((*_status)[v] != EVEN) continue;
3.912 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.913 + dualScale * _weight[a];
3.914 +
3.915 + if (minrw > rw) {
3.916 + min = _graph.oppositeArc(a);
3.917 + minrw = rw;
3.918 + }
3.919 + }
3.920 + if (min != INVALID) {
3.921 + _pred->set(node, min);
3.922 + _delta2->push(node, minrw);
3.923 + } else {
3.924 + _pred->set(node, INVALID);
3.925 + }
3.926 + }
3.927 +
3.928 + void alternatePath(Node even, int tree) {
3.929 + Node odd;
3.930 +
3.931 + _status->set(even, MATCHED);
3.932 + evenToMatched(even, tree);
3.933 +
3.934 + Arc prev = (*_matching)[even];
3.935 + while (prev != INVALID) {
3.936 + odd = _graph.target(prev);
3.937 + even = _graph.target((*_pred)[odd]);
3.938 + _matching->set(odd, (*_pred)[odd]);
3.939 + _status->set(odd, MATCHED);
3.940 + oddToMatched(odd);
3.941 +
3.942 + prev = (*_matching)[even];
3.943 + _status->set(even, MATCHED);
3.944 + _matching->set(even, _graph.oppositeArc((*_matching)[odd]));
3.945 + evenToMatched(even, tree);
3.946 + }
3.947 + }
3.948 +
3.949 + void destroyTree(int tree) {
3.950 + for (typename TreeSet::ItemIt n(*_tree_set, tree); n != INVALID; ++n) {
3.951 + if ((*_status)[n] == EVEN) {
3.952 + _status->set(n, MATCHED);
3.953 + evenToMatched(n, tree);
3.954 + } else if ((*_status)[n] == ODD) {
3.955 + _status->set(n, MATCHED);
3.956 + oddToMatched(n);
3.957 + }
3.958 + }
3.959 + _tree_set->eraseClass(tree);
3.960 + }
3.961 +
3.962 +
3.963 + void unmatchNode(const Node& node) {
3.964 + int tree = _tree_set->find(node);
3.965 +
3.966 + alternatePath(node, tree);
3.967 + destroyTree(tree);
3.968 +
3.969 + _matching->set(node, INVALID);
3.970 + }
3.971 +
3.972 +
3.973 + void augmentOnEdge(const Edge& edge) {
3.974 + Node left = _graph.u(edge);
3.975 + int left_tree = _tree_set->find(left);
3.976 +
3.977 + alternatePath(left, left_tree);
3.978 + destroyTree(left_tree);
3.979 + _matching->set(left, _graph.direct(edge, true));
3.980 +
3.981 + Node right = _graph.v(edge);
3.982 + int right_tree = _tree_set->find(right);
3.983 +
3.984 + alternatePath(right, right_tree);
3.985 + destroyTree(right_tree);
3.986 + _matching->set(right, _graph.direct(edge, false));
3.987 + }
3.988 +
3.989 + void augmentOnArc(const Arc& arc) {
3.990 + Node left = _graph.source(arc);
3.991 + _status->set(left, MATCHED);
3.992 + _matching->set(left, arc);
3.993 + _pred->set(left, arc);
3.994 +
3.995 + Node right = _graph.target(arc);
3.996 + int right_tree = _tree_set->find(right);
3.997 +
3.998 + alternatePath(right, right_tree);
3.999 + destroyTree(right_tree);
3.1000 + _matching->set(right, _graph.oppositeArc(arc));
3.1001 + }
3.1002 +
3.1003 + void extendOnArc(const Arc& arc) {
3.1004 + Node base = _graph.target(arc);
3.1005 + int tree = _tree_set->find(base);
3.1006 +
3.1007 + Node odd = _graph.source(arc);
3.1008 + _tree_set->insert(odd, tree);
3.1009 + _status->set(odd, ODD);
3.1010 + matchedToOdd(odd, tree);
3.1011 + _pred->set(odd, arc);
3.1012 +
3.1013 + Node even = _graph.target((*_matching)[odd]);
3.1014 + _tree_set->insert(even, tree);
3.1015 + _status->set(even, EVEN);
3.1016 + matchedToEven(even, tree);
3.1017 + }
3.1018 +
3.1019 + void cycleOnEdge(const Edge& edge, int tree) {
3.1020 + Node nca = INVALID;
3.1021 + std::vector<Node> left_path, right_path;
3.1022 +
3.1023 + {
3.1024 + std::set<Node> left_set, right_set;
3.1025 + Node left = _graph.u(edge);
3.1026 + left_path.push_back(left);
3.1027 + left_set.insert(left);
3.1028 +
3.1029 + Node right = _graph.v(edge);
3.1030 + right_path.push_back(right);
3.1031 + right_set.insert(right);
3.1032 +
3.1033 + while (true) {
3.1034 +
3.1035 + if (left_set.find(right) != left_set.end()) {
3.1036 + nca = right;
3.1037 + break;
3.1038 + }
3.1039 +
3.1040 + if ((*_matching)[left] == INVALID) break;
3.1041 +
3.1042 + left = _graph.target((*_matching)[left]);
3.1043 + left_path.push_back(left);
3.1044 + left = _graph.target((*_pred)[left]);
3.1045 + left_path.push_back(left);
3.1046 +
3.1047 + left_set.insert(left);
3.1048 +
3.1049 + if (right_set.find(left) != right_set.end()) {
3.1050 + nca = left;
3.1051 + break;
3.1052 + }
3.1053 +
3.1054 + if ((*_matching)[right] == INVALID) break;
3.1055 +
3.1056 + right = _graph.target((*_matching)[right]);
3.1057 + right_path.push_back(right);
3.1058 + right = _graph.target((*_pred)[right]);
3.1059 + right_path.push_back(right);
3.1060 +
3.1061 + right_set.insert(right);
3.1062 +
3.1063 + }
3.1064 +
3.1065 + if (nca == INVALID) {
3.1066 + if ((*_matching)[left] == INVALID) {
3.1067 + nca = right;
3.1068 + while (left_set.find(nca) == left_set.end()) {
3.1069 + nca = _graph.target((*_matching)[nca]);
3.1070 + right_path.push_back(nca);
3.1071 + nca = _graph.target((*_pred)[nca]);
3.1072 + right_path.push_back(nca);
3.1073 + }
3.1074 + } else {
3.1075 + nca = left;
3.1076 + while (right_set.find(nca) == right_set.end()) {
3.1077 + nca = _graph.target((*_matching)[nca]);
3.1078 + left_path.push_back(nca);
3.1079 + nca = _graph.target((*_pred)[nca]);
3.1080 + left_path.push_back(nca);
3.1081 + }
3.1082 + }
3.1083 + }
3.1084 + }
3.1085 +
3.1086 + alternatePath(nca, tree);
3.1087 + Arc prev;
3.1088 +
3.1089 + prev = _graph.direct(edge, true);
3.1090 + for (int i = 0; left_path[i] != nca; i += 2) {
3.1091 + _matching->set(left_path[i], prev);
3.1092 + _status->set(left_path[i], MATCHED);
3.1093 + evenToMatched(left_path[i], tree);
3.1094 +
3.1095 + prev = _graph.oppositeArc((*_pred)[left_path[i + 1]]);
3.1096 + _status->set(left_path[i + 1], MATCHED);
3.1097 + oddToMatched(left_path[i + 1]);
3.1098 + }
3.1099 + _matching->set(nca, prev);
3.1100 +
3.1101 + for (int i = 0; right_path[i] != nca; i += 2) {
3.1102 + _status->set(right_path[i], MATCHED);
3.1103 + evenToMatched(right_path[i], tree);
3.1104 +
3.1105 + _matching->set(right_path[i + 1], (*_pred)[right_path[i + 1]]);
3.1106 + _status->set(right_path[i + 1], MATCHED);
3.1107 + oddToMatched(right_path[i + 1]);
3.1108 + }
3.1109 +
3.1110 + destroyTree(tree);
3.1111 + }
3.1112 +
3.1113 + void extractCycle(const Arc &arc) {
3.1114 + Node left = _graph.source(arc);
3.1115 + Node odd = _graph.target((*_matching)[left]);
3.1116 + Arc prev;
3.1117 + while (odd != left) {
3.1118 + Node even = _graph.target((*_matching)[odd]);
3.1119 + prev = (*_matching)[odd];
3.1120 + odd = _graph.target((*_matching)[even]);
3.1121 + _matching->set(even, _graph.oppositeArc(prev));
3.1122 + }
3.1123 + _matching->set(left, arc);
3.1124 +
3.1125 + Node right = _graph.target(arc);
3.1126 + int right_tree = _tree_set->find(right);
3.1127 + alternatePath(right, right_tree);
3.1128 + destroyTree(right_tree);
3.1129 + _matching->set(right, _graph.oppositeArc(arc));
3.1130 + }
3.1131 +
3.1132 + public:
3.1133 +
3.1134 + /// \brief Constructor
3.1135 + ///
3.1136 + /// Constructor.
3.1137 + MaxWeightedFractionalMatching(const Graph& graph, const WeightMap& weight,
3.1138 + bool allow_loops = true)
3.1139 + : _graph(graph), _weight(weight), _matching(0),
3.1140 + _node_potential(0), _node_num(0), _allow_loops(allow_loops),
3.1141 + _status(0), _pred(0),
3.1142 + _tree_set_index(0), _tree_set(0),
3.1143 +
3.1144 + _delta1_index(0), _delta1(0),
3.1145 + _delta2_index(0), _delta2(0),
3.1146 + _delta3_index(0), _delta3(0),
3.1147 +
3.1148 + _delta_sum() {}
3.1149 +
3.1150 + ~MaxWeightedFractionalMatching() {
3.1151 + destroyStructures();
3.1152 + }
3.1153 +
3.1154 + /// \name Execution Control
3.1155 + /// The simplest way to execute the algorithm is to use the
3.1156 + /// \ref run() member function.
3.1157 +
3.1158 + ///@{
3.1159 +
3.1160 + /// \brief Initialize the algorithm
3.1161 + ///
3.1162 + /// This function initializes the algorithm.
3.1163 + void init() {
3.1164 + createStructures();
3.1165 +
3.1166 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1167 + (*_delta1_index)[n] = _delta1->PRE_HEAP;
3.1168 + (*_delta2_index)[n] = _delta2->PRE_HEAP;
3.1169 + }
3.1170 + for (EdgeIt e(_graph); e != INVALID; ++e) {
3.1171 + (*_delta3_index)[e] = _delta3->PRE_HEAP;
3.1172 + }
3.1173 +
3.1174 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1175 + Value max = 0;
3.1176 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
3.1177 + if (_graph.target(e) == n && !_allow_loops) continue;
3.1178 + if ((dualScale * _weight[e]) / 2 > max) {
3.1179 + max = (dualScale * _weight[e]) / 2;
3.1180 + }
3.1181 + }
3.1182 + _node_potential->set(n, max);
3.1183 + _delta1->push(n, max);
3.1184 +
3.1185 + _tree_set->insert(n);
3.1186 +
3.1187 + _matching->set(n, INVALID);
3.1188 + _status->set(n, EVEN);
3.1189 + }
3.1190 +
3.1191 + for (EdgeIt e(_graph); e != INVALID; ++e) {
3.1192 + Node left = _graph.u(e);
3.1193 + Node right = _graph.v(e);
3.1194 + if (left == right && !_allow_loops) continue;
3.1195 + _delta3->push(e, ((*_node_potential)[left] +
3.1196 + (*_node_potential)[right] -
3.1197 + dualScale * _weight[e]) / 2);
3.1198 + }
3.1199 + }
3.1200 +
3.1201 + /// \brief Start the algorithm
3.1202 + ///
3.1203 + /// This function starts the algorithm.
3.1204 + ///
3.1205 + /// \pre \ref init() must be called before using this function.
3.1206 + void start() {
3.1207 + enum OpType {
3.1208 + D1, D2, D3
3.1209 + };
3.1210 +
3.1211 + int unmatched = _node_num;
3.1212 + while (unmatched > 0) {
3.1213 + Value d1 = !_delta1->empty() ?
3.1214 + _delta1->prio() : std::numeric_limits<Value>::max();
3.1215 +
3.1216 + Value d2 = !_delta2->empty() ?
3.1217 + _delta2->prio() : std::numeric_limits<Value>::max();
3.1218 +
3.1219 + Value d3 = !_delta3->empty() ?
3.1220 + _delta3->prio() : std::numeric_limits<Value>::max();
3.1221 +
3.1222 + _delta_sum = d3; OpType ot = D3;
3.1223 + if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; }
3.1224 + if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
3.1225 +
3.1226 + switch (ot) {
3.1227 + case D1:
3.1228 + {
3.1229 + Node n = _delta1->top();
3.1230 + unmatchNode(n);
3.1231 + --unmatched;
3.1232 + }
3.1233 + break;
3.1234 + case D2:
3.1235 + {
3.1236 + Node n = _delta2->top();
3.1237 + Arc a = (*_pred)[n];
3.1238 + if ((*_matching)[n] == INVALID) {
3.1239 + augmentOnArc(a);
3.1240 + --unmatched;
3.1241 + } else {
3.1242 + Node v = _graph.target((*_matching)[n]);
3.1243 + if ((*_matching)[n] !=
3.1244 + _graph.oppositeArc((*_matching)[v])) {
3.1245 + extractCycle(a);
3.1246 + --unmatched;
3.1247 + } else {
3.1248 + extendOnArc(a);
3.1249 + }
3.1250 + }
3.1251 + } break;
3.1252 + case D3:
3.1253 + {
3.1254 + Edge e = _delta3->top();
3.1255 +
3.1256 + Node left = _graph.u(e);
3.1257 + Node right = _graph.v(e);
3.1258 +
3.1259 + int left_tree = _tree_set->find(left);
3.1260 + int right_tree = _tree_set->find(right);
3.1261 +
3.1262 + if (left_tree == right_tree) {
3.1263 + cycleOnEdge(e, left_tree);
3.1264 + --unmatched;
3.1265 + } else {
3.1266 + augmentOnEdge(e);
3.1267 + unmatched -= 2;
3.1268 + }
3.1269 + } break;
3.1270 + }
3.1271 + }
3.1272 + }
3.1273 +
3.1274 + /// \brief Run the algorithm.
3.1275 + ///
3.1276 + /// This method runs the \c %MaxWeightedMatching algorithm.
3.1277 + ///
3.1278 + /// \note mwfm.run() is just a shortcut of the following code.
3.1279 + /// \code
3.1280 + /// mwfm.init();
3.1281 + /// mwfm.start();
3.1282 + /// \endcode
3.1283 + void run() {
3.1284 + init();
3.1285 + start();
3.1286 + }
3.1287 +
3.1288 + /// @}
3.1289 +
3.1290 + /// \name Primal Solution
3.1291 + /// Functions to get the primal solution, i.e. the maximum weighted
3.1292 + /// matching.\n
3.1293 + /// Either \ref run() or \ref start() function should be called before
3.1294 + /// using them.
3.1295 +
3.1296 + /// @{
3.1297 +
3.1298 + /// \brief Return the weight of the matching.
3.1299 + ///
3.1300 + /// This function returns the weight of the found matching. This
3.1301 + /// value is scaled by \ref primalScale "primal scale".
3.1302 + ///
3.1303 + /// \pre Either run() or start() must be called before using this function.
3.1304 + Value matchingWeight() const {
3.1305 + Value sum = 0;
3.1306 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1307 + if ((*_matching)[n] != INVALID) {
3.1308 + sum += _weight[(*_matching)[n]];
3.1309 + }
3.1310 + }
3.1311 + return sum * primalScale / 2;
3.1312 + }
3.1313 +
3.1314 + /// \brief Return the number of covered nodes in the matching.
3.1315 + ///
3.1316 + /// This function returns the number of covered nodes in the matching.
3.1317 + ///
3.1318 + /// \pre Either run() or start() must be called before using this function.
3.1319 + int matchingSize() const {
3.1320 + int num = 0;
3.1321 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1322 + if ((*_matching)[n] != INVALID) {
3.1323 + ++num;
3.1324 + }
3.1325 + }
3.1326 + return num;
3.1327 + }
3.1328 +
3.1329 + /// \brief Return \c true if the given edge is in the matching.
3.1330 + ///
3.1331 + /// This function returns \c true if the given edge is in the
3.1332 + /// found matching. The result is scaled by \ref primalScale
3.1333 + /// "primal scale".
3.1334 + ///
3.1335 + /// \pre Either run() or start() must be called before using this function.
3.1336 + Value matching(const Edge& edge) const {
3.1337 + return Value(edge == (*_matching)[_graph.u(edge)] ? 1 : 0)
3.1338 + * primalScale / 2 + Value(edge == (*_matching)[_graph.v(edge)] ? 1 : 0)
3.1339 + * primalScale / 2;
3.1340 + }
3.1341 +
3.1342 + /// \brief Return the fractional matching arc (or edge) incident
3.1343 + /// to the given node.
3.1344 + ///
3.1345 + /// This function returns one of the fractional matching arc (or
3.1346 + /// edge) incident to the given node in the found matching or \c
3.1347 + /// INVALID if the node is not covered by the matching or if the
3.1348 + /// node is on an odd length cycle then it is the successor edge
3.1349 + /// on the cycle.
3.1350 + ///
3.1351 + /// \pre Either run() or start() must be called before using this function.
3.1352 + Arc matching(const Node& node) const {
3.1353 + return (*_matching)[node];
3.1354 + }
3.1355 +
3.1356 + /// \brief Return a const reference to the matching map.
3.1357 + ///
3.1358 + /// This function returns a const reference to a node map that stores
3.1359 + /// the matching arc (or edge) incident to each node.
3.1360 + const MatchingMap& matchingMap() const {
3.1361 + return *_matching;
3.1362 + }
3.1363 +
3.1364 + /// @}
3.1365 +
3.1366 + /// \name Dual Solution
3.1367 + /// Functions to get the dual solution.\n
3.1368 + /// Either \ref run() or \ref start() function should be called before
3.1369 + /// using them.
3.1370 +
3.1371 + /// @{
3.1372 +
3.1373 + /// \brief Return the value of the dual solution.
3.1374 + ///
3.1375 + /// This function returns the value of the dual solution.
3.1376 + /// It should be equal to the primal value scaled by \ref dualScale
3.1377 + /// "dual scale".
3.1378 + ///
3.1379 + /// \pre Either run() or start() must be called before using this function.
3.1380 + Value dualValue() const {
3.1381 + Value sum = 0;
3.1382 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1383 + sum += nodeValue(n);
3.1384 + }
3.1385 + return sum;
3.1386 + }
3.1387 +
3.1388 + /// \brief Return the dual value (potential) of the given node.
3.1389 + ///
3.1390 + /// This function returns the dual value (potential) of the given node.
3.1391 + ///
3.1392 + /// \pre Either run() or start() must be called before using this function.
3.1393 + Value nodeValue(const Node& n) const {
3.1394 + return (*_node_potential)[n];
3.1395 + }
3.1396 +
3.1397 + /// @}
3.1398 +
3.1399 + };
3.1400 +
3.1401 + /// \ingroup matching
3.1402 + ///
3.1403 + /// \brief Weighted fractional perfect matching in general graphs
3.1404 + ///
3.1405 + /// This class provides an efficient implementation of fractional
3.1406 + /// matching algorithm. The implementation is based on extensive use
3.1407 + /// of priority queues and provides \f$O(nm\log n)\f$ time
3.1408 + /// complexity.
3.1409 + ///
3.1410 + /// The maximum weighted fractional perfect matching is a relaxation
3.1411 + /// of the maximum weighted perfect matching problem where the odd
3.1412 + /// set constraints are omitted.
3.1413 + /// It can be formulated with the following linear program.
3.1414 + /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
3.1415 + /// \f[x_e \ge 0\quad \forall e\in E\f]
3.1416 + /// \f[\max \sum_{e\in E}x_ew_e\f]
3.1417 + /// where \f$\delta(X)\f$ is the set of edges incident to a node in
3.1418 + /// \f$X\f$. The result must be the union of a matching with one
3.1419 + /// value edges and a set of odd length cycles with half value edges.
3.1420 + ///
3.1421 + /// The algorithm calculates an optimal fractional matching and a
3.1422 + /// proof of the optimality. The solution of the dual problem can be
3.1423 + /// used to check the result of the algorithm. The dual linear
3.1424 + /// problem is the following.
3.1425 + /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f]
3.1426 + /// \f[\min \sum_{u \in V}y_u \f] ///
3.1427 + ///
3.1428 + /// The algorithm can be executed with the run() function.
3.1429 + /// After it the matching (the primal solution) and the dual solution
3.1430 + /// can be obtained using the query functions.
3.1431 +
3.1432 + /// If the value type is integer, then the primal and the dual
3.1433 + /// solutions are multiplied by
3.1434 + /// \ref MaxWeightedMatching::primalScale "2" and
3.1435 + /// \ref MaxWeightedMatching::dualScale "4" respectively.
3.1436 + ///
3.1437 + /// \tparam GR The undirected graph type the algorithm runs on.
3.1438 + /// \tparam WM The type edge weight map. The default type is
3.1439 + /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
3.1440 +#ifdef DOXYGEN
3.1441 + template <typename GR, typename WM>
3.1442 +#else
3.1443 + template <typename GR,
3.1444 + typename WM = typename GR::template EdgeMap<int> >
3.1445 +#endif
3.1446 + class MaxWeightedPerfectFractionalMatching {
3.1447 + public:
3.1448 +
3.1449 + /// The graph type of the algorithm
3.1450 + typedef GR Graph;
3.1451 + /// The type of the edge weight map
3.1452 + typedef WM WeightMap;
3.1453 + /// The value type of the edge weights
3.1454 + typedef typename WeightMap::Value Value;
3.1455 +
3.1456 + /// The type of the matching map
3.1457 + typedef typename Graph::template NodeMap<typename Graph::Arc>
3.1458 + MatchingMap;
3.1459 +
3.1460 + /// \brief Scaling factor for primal solution
3.1461 + ///
3.1462 + /// Scaling factor for primal solution. It is equal to 2 or 1
3.1463 + /// according to the value type.
3.1464 + static const int primalScale =
3.1465 + std::numeric_limits<Value>::is_integer ? 2 : 1;
3.1466 +
3.1467 + /// \brief Scaling factor for dual solution
3.1468 + ///
3.1469 + /// Scaling factor for dual solution. It is equal to 4 or 1
3.1470 + /// according to the value type.
3.1471 + static const int dualScale =
3.1472 + std::numeric_limits<Value>::is_integer ? 4 : 1;
3.1473 +
3.1474 + private:
3.1475 +
3.1476 + TEMPLATE_GRAPH_TYPEDEFS(Graph);
3.1477 +
3.1478 + typedef typename Graph::template NodeMap<Value> NodePotential;
3.1479 +
3.1480 + const Graph& _graph;
3.1481 + const WeightMap& _weight;
3.1482 +
3.1483 + MatchingMap* _matching;
3.1484 + NodePotential* _node_potential;
3.1485 +
3.1486 + int _node_num;
3.1487 + bool _allow_loops;
3.1488 +
3.1489 + enum Status {
3.1490 + EVEN = -1, MATCHED = 0, ODD = 1
3.1491 + };
3.1492 +
3.1493 + typedef typename Graph::template NodeMap<Status> StatusMap;
3.1494 + StatusMap* _status;
3.1495 +
3.1496 + typedef typename Graph::template NodeMap<Arc> PredMap;
3.1497 + PredMap* _pred;
3.1498 +
3.1499 + typedef ExtendFindEnum<IntNodeMap> TreeSet;
3.1500 +
3.1501 + IntNodeMap *_tree_set_index;
3.1502 + TreeSet *_tree_set;
3.1503 +
3.1504 + IntNodeMap *_delta2_index;
3.1505 + BinHeap<Value, IntNodeMap> *_delta2;
3.1506 +
3.1507 + IntEdgeMap *_delta3_index;
3.1508 + BinHeap<Value, IntEdgeMap> *_delta3;
3.1509 +
3.1510 + Value _delta_sum;
3.1511 +
3.1512 + void createStructures() {
3.1513 + _node_num = countNodes(_graph);
3.1514 +
3.1515 + if (!_matching) {
3.1516 + _matching = new MatchingMap(_graph);
3.1517 + }
3.1518 + if (!_node_potential) {
3.1519 + _node_potential = new NodePotential(_graph);
3.1520 + }
3.1521 + if (!_status) {
3.1522 + _status = new StatusMap(_graph);
3.1523 + }
3.1524 + if (!_pred) {
3.1525 + _pred = new PredMap(_graph);
3.1526 + }
3.1527 + if (!_tree_set) {
3.1528 + _tree_set_index = new IntNodeMap(_graph);
3.1529 + _tree_set = new TreeSet(*_tree_set_index);
3.1530 + }
3.1531 + if (!_delta2) {
3.1532 + _delta2_index = new IntNodeMap(_graph);
3.1533 + _delta2 = new BinHeap<Value, IntNodeMap>(*_delta2_index);
3.1534 + }
3.1535 + if (!_delta3) {
3.1536 + _delta3_index = new IntEdgeMap(_graph);
3.1537 + _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
3.1538 + }
3.1539 + }
3.1540 +
3.1541 + void destroyStructures() {
3.1542 + if (_matching) {
3.1543 + delete _matching;
3.1544 + }
3.1545 + if (_node_potential) {
3.1546 + delete _node_potential;
3.1547 + }
3.1548 + if (_status) {
3.1549 + delete _status;
3.1550 + }
3.1551 + if (_pred) {
3.1552 + delete _pred;
3.1553 + }
3.1554 + if (_tree_set) {
3.1555 + delete _tree_set_index;
3.1556 + delete _tree_set;
3.1557 + }
3.1558 + if (_delta2) {
3.1559 + delete _delta2_index;
3.1560 + delete _delta2;
3.1561 + }
3.1562 + if (_delta3) {
3.1563 + delete _delta3_index;
3.1564 + delete _delta3;
3.1565 + }
3.1566 + }
3.1567 +
3.1568 + void matchedToEven(Node node, int tree) {
3.1569 + _tree_set->insert(node, tree);
3.1570 + _node_potential->set(node, (*_node_potential)[node] + _delta_sum);
3.1571 +
3.1572 + if (_delta2->state(node) == _delta2->IN_HEAP) {
3.1573 + _delta2->erase(node);
3.1574 + }
3.1575 +
3.1576 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.1577 + Node v = _graph.source(a);
3.1578 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.1579 + dualScale * _weight[a];
3.1580 + if (node == v) {
3.1581 + if (_allow_loops && _graph.direction(a)) {
3.1582 + _delta3->push(a, rw / 2);
3.1583 + }
3.1584 + } else if ((*_status)[v] == EVEN) {
3.1585 + _delta3->push(a, rw / 2);
3.1586 + } else if ((*_status)[v] == MATCHED) {
3.1587 + if (_delta2->state(v) != _delta2->IN_HEAP) {
3.1588 + _pred->set(v, a);
3.1589 + _delta2->push(v, rw);
3.1590 + } else if ((*_delta2)[v] > rw) {
3.1591 + _pred->set(v, a);
3.1592 + _delta2->decrease(v, rw);
3.1593 + }
3.1594 + }
3.1595 + }
3.1596 + }
3.1597 +
3.1598 + void matchedToOdd(Node node, int tree) {
3.1599 + _tree_set->insert(node, tree);
3.1600 + _node_potential->set(node, (*_node_potential)[node] - _delta_sum);
3.1601 +
3.1602 + if (_delta2->state(node) == _delta2->IN_HEAP) {
3.1603 + _delta2->erase(node);
3.1604 + }
3.1605 + }
3.1606 +
3.1607 + void evenToMatched(Node node, int tree) {
3.1608 + _node_potential->set(node, (*_node_potential)[node] - _delta_sum);
3.1609 + Arc min = INVALID;
3.1610 + Value minrw = std::numeric_limits<Value>::max();
3.1611 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.1612 + Node v = _graph.source(a);
3.1613 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.1614 + dualScale * _weight[a];
3.1615 +
3.1616 + if (node == v) {
3.1617 + if (_allow_loops && _graph.direction(a)) {
3.1618 + _delta3->erase(a);
3.1619 + }
3.1620 + } else if ((*_status)[v] == EVEN) {
3.1621 + _delta3->erase(a);
3.1622 + if (minrw > rw) {
3.1623 + min = _graph.oppositeArc(a);
3.1624 + minrw = rw;
3.1625 + }
3.1626 + } else if ((*_status)[v] == MATCHED) {
3.1627 + if ((*_pred)[v] == a) {
3.1628 + Arc mina = INVALID;
3.1629 + Value minrwa = std::numeric_limits<Value>::max();
3.1630 + for (OutArcIt aa(_graph, v); aa != INVALID; ++aa) {
3.1631 + Node va = _graph.target(aa);
3.1632 + if ((*_status)[va] != EVEN ||
3.1633 + _tree_set->find(va) == tree) continue;
3.1634 + Value rwa = (*_node_potential)[v] + (*_node_potential)[va] -
3.1635 + dualScale * _weight[aa];
3.1636 + if (minrwa > rwa) {
3.1637 + minrwa = rwa;
3.1638 + mina = aa;
3.1639 + }
3.1640 + }
3.1641 + if (mina != INVALID) {
3.1642 + _pred->set(v, mina);
3.1643 + _delta2->increase(v, minrwa);
3.1644 + } else {
3.1645 + _pred->set(v, INVALID);
3.1646 + _delta2->erase(v);
3.1647 + }
3.1648 + }
3.1649 + }
3.1650 + }
3.1651 + if (min != INVALID) {
3.1652 + _pred->set(node, min);
3.1653 + _delta2->push(node, minrw);
3.1654 + } else {
3.1655 + _pred->set(node, INVALID);
3.1656 + }
3.1657 + }
3.1658 +
3.1659 + void oddToMatched(Node node) {
3.1660 + _node_potential->set(node, (*_node_potential)[node] + _delta_sum);
3.1661 + Arc min = INVALID;
3.1662 + Value minrw = std::numeric_limits<Value>::max();
3.1663 + for (InArcIt a(_graph, node); a != INVALID; ++a) {
3.1664 + Node v = _graph.source(a);
3.1665 + if ((*_status)[v] != EVEN) continue;
3.1666 + Value rw = (*_node_potential)[node] + (*_node_potential)[v] -
3.1667 + dualScale * _weight[a];
3.1668 +
3.1669 + if (minrw > rw) {
3.1670 + min = _graph.oppositeArc(a);
3.1671 + minrw = rw;
3.1672 + }
3.1673 + }
3.1674 + if (min != INVALID) {
3.1675 + _pred->set(node, min);
3.1676 + _delta2->push(node, minrw);
3.1677 + } else {
3.1678 + _pred->set(node, INVALID);
3.1679 + }
3.1680 + }
3.1681 +
3.1682 + void alternatePath(Node even, int tree) {
3.1683 + Node odd;
3.1684 +
3.1685 + _status->set(even, MATCHED);
3.1686 + evenToMatched(even, tree);
3.1687 +
3.1688 + Arc prev = (*_matching)[even];
3.1689 + while (prev != INVALID) {
3.1690 + odd = _graph.target(prev);
3.1691 + even = _graph.target((*_pred)[odd]);
3.1692 + _matching->set(odd, (*_pred)[odd]);
3.1693 + _status->set(odd, MATCHED);
3.1694 + oddToMatched(odd);
3.1695 +
3.1696 + prev = (*_matching)[even];
3.1697 + _status->set(even, MATCHED);
3.1698 + _matching->set(even, _graph.oppositeArc((*_matching)[odd]));
3.1699 + evenToMatched(even, tree);
3.1700 + }
3.1701 + }
3.1702 +
3.1703 + void destroyTree(int tree) {
3.1704 + for (typename TreeSet::ItemIt n(*_tree_set, tree); n != INVALID; ++n) {
3.1705 + if ((*_status)[n] == EVEN) {
3.1706 + _status->set(n, MATCHED);
3.1707 + evenToMatched(n, tree);
3.1708 + } else if ((*_status)[n] == ODD) {
3.1709 + _status->set(n, MATCHED);
3.1710 + oddToMatched(n);
3.1711 + }
3.1712 + }
3.1713 + _tree_set->eraseClass(tree);
3.1714 + }
3.1715 +
3.1716 + void augmentOnEdge(const Edge& edge) {
3.1717 + Node left = _graph.u(edge);
3.1718 + int left_tree = _tree_set->find(left);
3.1719 +
3.1720 + alternatePath(left, left_tree);
3.1721 + destroyTree(left_tree);
3.1722 + _matching->set(left, _graph.direct(edge, true));
3.1723 +
3.1724 + Node right = _graph.v(edge);
3.1725 + int right_tree = _tree_set->find(right);
3.1726 +
3.1727 + alternatePath(right, right_tree);
3.1728 + destroyTree(right_tree);
3.1729 + _matching->set(right, _graph.direct(edge, false));
3.1730 + }
3.1731 +
3.1732 + void augmentOnArc(const Arc& arc) {
3.1733 + Node left = _graph.source(arc);
3.1734 + _status->set(left, MATCHED);
3.1735 + _matching->set(left, arc);
3.1736 + _pred->set(left, arc);
3.1737 +
3.1738 + Node right = _graph.target(arc);
3.1739 + int right_tree = _tree_set->find(right);
3.1740 +
3.1741 + alternatePath(right, right_tree);
3.1742 + destroyTree(right_tree);
3.1743 + _matching->set(right, _graph.oppositeArc(arc));
3.1744 + }
3.1745 +
3.1746 + void extendOnArc(const Arc& arc) {
3.1747 + Node base = _graph.target(arc);
3.1748 + int tree = _tree_set->find(base);
3.1749 +
3.1750 + Node odd = _graph.source(arc);
3.1751 + _tree_set->insert(odd, tree);
3.1752 + _status->set(odd, ODD);
3.1753 + matchedToOdd(odd, tree);
3.1754 + _pred->set(odd, arc);
3.1755 +
3.1756 + Node even = _graph.target((*_matching)[odd]);
3.1757 + _tree_set->insert(even, tree);
3.1758 + _status->set(even, EVEN);
3.1759 + matchedToEven(even, tree);
3.1760 + }
3.1761 +
3.1762 + void cycleOnEdge(const Edge& edge, int tree) {
3.1763 + Node nca = INVALID;
3.1764 + std::vector<Node> left_path, right_path;
3.1765 +
3.1766 + {
3.1767 + std::set<Node> left_set, right_set;
3.1768 + Node left = _graph.u(edge);
3.1769 + left_path.push_back(left);
3.1770 + left_set.insert(left);
3.1771 +
3.1772 + Node right = _graph.v(edge);
3.1773 + right_path.push_back(right);
3.1774 + right_set.insert(right);
3.1775 +
3.1776 + while (true) {
3.1777 +
3.1778 + if (left_set.find(right) != left_set.end()) {
3.1779 + nca = right;
3.1780 + break;
3.1781 + }
3.1782 +
3.1783 + if ((*_matching)[left] == INVALID) break;
3.1784 +
3.1785 + left = _graph.target((*_matching)[left]);
3.1786 + left_path.push_back(left);
3.1787 + left = _graph.target((*_pred)[left]);
3.1788 + left_path.push_back(left);
3.1789 +
3.1790 + left_set.insert(left);
3.1791 +
3.1792 + if (right_set.find(left) != right_set.end()) {
3.1793 + nca = left;
3.1794 + break;
3.1795 + }
3.1796 +
3.1797 + if ((*_matching)[right] == INVALID) break;
3.1798 +
3.1799 + right = _graph.target((*_matching)[right]);
3.1800 + right_path.push_back(right);
3.1801 + right = _graph.target((*_pred)[right]);
3.1802 + right_path.push_back(right);
3.1803 +
3.1804 + right_set.insert(right);
3.1805 +
3.1806 + }
3.1807 +
3.1808 + if (nca == INVALID) {
3.1809 + if ((*_matching)[left] == INVALID) {
3.1810 + nca = right;
3.1811 + while (left_set.find(nca) == left_set.end()) {
3.1812 + nca = _graph.target((*_matching)[nca]);
3.1813 + right_path.push_back(nca);
3.1814 + nca = _graph.target((*_pred)[nca]);
3.1815 + right_path.push_back(nca);
3.1816 + }
3.1817 + } else {
3.1818 + nca = left;
3.1819 + while (right_set.find(nca) == right_set.end()) {
3.1820 + nca = _graph.target((*_matching)[nca]);
3.1821 + left_path.push_back(nca);
3.1822 + nca = _graph.target((*_pred)[nca]);
3.1823 + left_path.push_back(nca);
3.1824 + }
3.1825 + }
3.1826 + }
3.1827 + }
3.1828 +
3.1829 + alternatePath(nca, tree);
3.1830 + Arc prev;
3.1831 +
3.1832 + prev = _graph.direct(edge, true);
3.1833 + for (int i = 0; left_path[i] != nca; i += 2) {
3.1834 + _matching->set(left_path[i], prev);
3.1835 + _status->set(left_path[i], MATCHED);
3.1836 + evenToMatched(left_path[i], tree);
3.1837 +
3.1838 + prev = _graph.oppositeArc((*_pred)[left_path[i + 1]]);
3.1839 + _status->set(left_path[i + 1], MATCHED);
3.1840 + oddToMatched(left_path[i + 1]);
3.1841 + }
3.1842 + _matching->set(nca, prev);
3.1843 +
3.1844 + for (int i = 0; right_path[i] != nca; i += 2) {
3.1845 + _status->set(right_path[i], MATCHED);
3.1846 + evenToMatched(right_path[i], tree);
3.1847 +
3.1848 + _matching->set(right_path[i + 1], (*_pred)[right_path[i + 1]]);
3.1849 + _status->set(right_path[i + 1], MATCHED);
3.1850 + oddToMatched(right_path[i + 1]);
3.1851 + }
3.1852 +
3.1853 + destroyTree(tree);
3.1854 + }
3.1855 +
3.1856 + void extractCycle(const Arc &arc) {
3.1857 + Node left = _graph.source(arc);
3.1858 + Node odd = _graph.target((*_matching)[left]);
3.1859 + Arc prev;
3.1860 + while (odd != left) {
3.1861 + Node even = _graph.target((*_matching)[odd]);
3.1862 + prev = (*_matching)[odd];
3.1863 + odd = _graph.target((*_matching)[even]);
3.1864 + _matching->set(even, _graph.oppositeArc(prev));
3.1865 + }
3.1866 + _matching->set(left, arc);
3.1867 +
3.1868 + Node right = _graph.target(arc);
3.1869 + int right_tree = _tree_set->find(right);
3.1870 + alternatePath(right, right_tree);
3.1871 + destroyTree(right_tree);
3.1872 + _matching->set(right, _graph.oppositeArc(arc));
3.1873 + }
3.1874 +
3.1875 + public:
3.1876 +
3.1877 + /// \brief Constructor
3.1878 + ///
3.1879 + /// Constructor.
3.1880 + MaxWeightedPerfectFractionalMatching(const Graph& graph,
3.1881 + const WeightMap& weight,
3.1882 + bool allow_loops = true)
3.1883 + : _graph(graph), _weight(weight), _matching(0),
3.1884 + _node_potential(0), _node_num(0), _allow_loops(allow_loops),
3.1885 + _status(0), _pred(0),
3.1886 + _tree_set_index(0), _tree_set(0),
3.1887 +
3.1888 + _delta2_index(0), _delta2(0),
3.1889 + _delta3_index(0), _delta3(0),
3.1890 +
3.1891 + _delta_sum() {}
3.1892 +
3.1893 + ~MaxWeightedPerfectFractionalMatching() {
3.1894 + destroyStructures();
3.1895 + }
3.1896 +
3.1897 + /// \name Execution Control
3.1898 + /// The simplest way to execute the algorithm is to use the
3.1899 + /// \ref run() member function.
3.1900 +
3.1901 + ///@{
3.1902 +
3.1903 + /// \brief Initialize the algorithm
3.1904 + ///
3.1905 + /// This function initializes the algorithm.
3.1906 + void init() {
3.1907 + createStructures();
3.1908 +
3.1909 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1910 + (*_delta2_index)[n] = _delta2->PRE_HEAP;
3.1911 + }
3.1912 + for (EdgeIt e(_graph); e != INVALID; ++e) {
3.1913 + (*_delta3_index)[e] = _delta3->PRE_HEAP;
3.1914 + }
3.1915 +
3.1916 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.1917 + Value max = - std::numeric_limits<Value>::max();
3.1918 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
3.1919 + if (_graph.target(e) == n && !_allow_loops) continue;
3.1920 + if ((dualScale * _weight[e]) / 2 > max) {
3.1921 + max = (dualScale * _weight[e]) / 2;
3.1922 + }
3.1923 + }
3.1924 + _node_potential->set(n, max);
3.1925 +
3.1926 + _tree_set->insert(n);
3.1927 +
3.1928 + _matching->set(n, INVALID);
3.1929 + _status->set(n, EVEN);
3.1930 + }
3.1931 +
3.1932 + for (EdgeIt e(_graph); e != INVALID; ++e) {
3.1933 + Node left = _graph.u(e);
3.1934 + Node right = _graph.v(e);
3.1935 + if (left == right && !_allow_loops) continue;
3.1936 + _delta3->push(e, ((*_node_potential)[left] +
3.1937 + (*_node_potential)[right] -
3.1938 + dualScale * _weight[e]) / 2);
3.1939 + }
3.1940 + }
3.1941 +
3.1942 + /// \brief Start the algorithm
3.1943 + ///
3.1944 + /// This function starts the algorithm.
3.1945 + ///
3.1946 + /// \pre \ref init() must be called before using this function.
3.1947 + bool start() {
3.1948 + enum OpType {
3.1949 + D2, D3
3.1950 + };
3.1951 +
3.1952 + int unmatched = _node_num;
3.1953 + while (unmatched > 0) {
3.1954 + Value d2 = !_delta2->empty() ?
3.1955 + _delta2->prio() : std::numeric_limits<Value>::max();
3.1956 +
3.1957 + Value d3 = !_delta3->empty() ?
3.1958 + _delta3->prio() : std::numeric_limits<Value>::max();
3.1959 +
3.1960 + _delta_sum = d3; OpType ot = D3;
3.1961 + if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
3.1962 +
3.1963 + if (_delta_sum == std::numeric_limits<Value>::max()) {
3.1964 + return false;
3.1965 + }
3.1966 +
3.1967 + switch (ot) {
3.1968 + case D2:
3.1969 + {
3.1970 + Node n = _delta2->top();
3.1971 + Arc a = (*_pred)[n];
3.1972 + if ((*_matching)[n] == INVALID) {
3.1973 + augmentOnArc(a);
3.1974 + --unmatched;
3.1975 + } else {
3.1976 + Node v = _graph.target((*_matching)[n]);
3.1977 + if ((*_matching)[n] !=
3.1978 + _graph.oppositeArc((*_matching)[v])) {
3.1979 + extractCycle(a);
3.1980 + --unmatched;
3.1981 + } else {
3.1982 + extendOnArc(a);
3.1983 + }
3.1984 + }
3.1985 + } break;
3.1986 + case D3:
3.1987 + {
3.1988 + Edge e = _delta3->top();
3.1989 +
3.1990 + Node left = _graph.u(e);
3.1991 + Node right = _graph.v(e);
3.1992 +
3.1993 + int left_tree = _tree_set->find(left);
3.1994 + int right_tree = _tree_set->find(right);
3.1995 +
3.1996 + if (left_tree == right_tree) {
3.1997 + cycleOnEdge(e, left_tree);
3.1998 + --unmatched;
3.1999 + } else {
3.2000 + augmentOnEdge(e);
3.2001 + unmatched -= 2;
3.2002 + }
3.2003 + } break;
3.2004 + }
3.2005 + }
3.2006 + return true;
3.2007 + }
3.2008 +
3.2009 + /// \brief Run the algorithm.
3.2010 + ///
3.2011 + /// This method runs the \c %MaxWeightedMatching algorithm.
3.2012 + ///
3.2013 + /// \note mwfm.run() is just a shortcut of the following code.
3.2014 + /// \code
3.2015 + /// mwpfm.init();
3.2016 + /// mwpfm.start();
3.2017 + /// \endcode
3.2018 + bool run() {
3.2019 + init();
3.2020 + return start();
3.2021 + }
3.2022 +
3.2023 + /// @}
3.2024 +
3.2025 + /// \name Primal Solution
3.2026 + /// Functions to get the primal solution, i.e. the maximum weighted
3.2027 + /// matching.\n
3.2028 + /// Either \ref run() or \ref start() function should be called before
3.2029 + /// using them.
3.2030 +
3.2031 + /// @{
3.2032 +
3.2033 + /// \brief Return the weight of the matching.
3.2034 + ///
3.2035 + /// This function returns the weight of the found matching. This
3.2036 + /// value is scaled by \ref primalScale "primal scale".
3.2037 + ///
3.2038 + /// \pre Either run() or start() must be called before using this function.
3.2039 + Value matchingWeight() const {
3.2040 + Value sum = 0;
3.2041 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.2042 + if ((*_matching)[n] != INVALID) {
3.2043 + sum += _weight[(*_matching)[n]];
3.2044 + }
3.2045 + }
3.2046 + return sum * primalScale / 2;
3.2047 + }
3.2048 +
3.2049 + /// \brief Return the number of covered nodes in the matching.
3.2050 + ///
3.2051 + /// This function returns the number of covered nodes in the matching.
3.2052 + ///
3.2053 + /// \pre Either run() or start() must be called before using this function.
3.2054 + int matchingSize() const {
3.2055 + int num = 0;
3.2056 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.2057 + if ((*_matching)[n] != INVALID) {
3.2058 + ++num;
3.2059 + }
3.2060 + }
3.2061 + return num;
3.2062 + }
3.2063 +
3.2064 + /// \brief Return \c true if the given edge is in the matching.
3.2065 + ///
3.2066 + /// This function returns \c true if the given edge is in the
3.2067 + /// found matching. The result is scaled by \ref primalScale
3.2068 + /// "primal scale".
3.2069 + ///
3.2070 + /// \pre Either run() or start() must be called before using this function.
3.2071 + Value matching(const Edge& edge) const {
3.2072 + return Value(edge == (*_matching)[_graph.u(edge)] ? 1 : 0)
3.2073 + * primalScale / 2 + Value(edge == (*_matching)[_graph.v(edge)] ? 1 : 0)
3.2074 + * primalScale / 2;
3.2075 + }
3.2076 +
3.2077 + /// \brief Return the fractional matching arc (or edge) incident
3.2078 + /// to the given node.
3.2079 + ///
3.2080 + /// This function returns one of the fractional matching arc (or
3.2081 + /// edge) incident to the given node in the found matching or \c
3.2082 + /// INVALID if the node is not covered by the matching or if the
3.2083 + /// node is on an odd length cycle then it is the successor edge
3.2084 + /// on the cycle.
3.2085 + ///
3.2086 + /// \pre Either run() or start() must be called before using this function.
3.2087 + Arc matching(const Node& node) const {
3.2088 + return (*_matching)[node];
3.2089 + }
3.2090 +
3.2091 + /// \brief Return a const reference to the matching map.
3.2092 + ///
3.2093 + /// This function returns a const reference to a node map that stores
3.2094 + /// the matching arc (or edge) incident to each node.
3.2095 + const MatchingMap& matchingMap() const {
3.2096 + return *_matching;
3.2097 + }
3.2098 +
3.2099 + /// @}
3.2100 +
3.2101 + /// \name Dual Solution
3.2102 + /// Functions to get the dual solution.\n
3.2103 + /// Either \ref run() or \ref start() function should be called before
3.2104 + /// using them.
3.2105 +
3.2106 + /// @{
3.2107 +
3.2108 + /// \brief Return the value of the dual solution.
3.2109 + ///
3.2110 + /// This function returns the value of the dual solution.
3.2111 + /// It should be equal to the primal value scaled by \ref dualScale
3.2112 + /// "dual scale".
3.2113 + ///
3.2114 + /// \pre Either run() or start() must be called before using this function.
3.2115 + Value dualValue() const {
3.2116 + Value sum = 0;
3.2117 + for (NodeIt n(_graph); n != INVALID; ++n) {
3.2118 + sum += nodeValue(n);
3.2119 + }
3.2120 + return sum;
3.2121 + }
3.2122 +
3.2123 + /// \brief Return the dual value (potential) of the given node.
3.2124 + ///
3.2125 + /// This function returns the dual value (potential) of the given node.
3.2126 + ///
3.2127 + /// \pre Either run() or start() must be called before using this function.
3.2128 + Value nodeValue(const Node& n) const {
3.2129 + return (*_node_potential)[n];
3.2130 + }
3.2131 +
3.2132 + /// @}
3.2133 +
3.2134 + };
3.2135 +
3.2136 +} //END OF NAMESPACE LEMON
3.2137 +
3.2138 +#endif //LEMON_FRACTIONAL_MATCHING_H
4.1 --- a/test/CMakeLists.txt Sun Sep 20 21:38:24 2009 +0200
4.2 +++ b/test/CMakeLists.txt Fri Sep 25 21:51:36 2009 +0200
4.3 @@ -21,6 +21,7 @@
4.4 edge_set_test
4.5 error_test
4.6 euler_test
4.7 + fractional_matching_test
4.8 gomory_hu_test
4.9 graph_copy_test
4.10 graph_test
5.1 --- a/test/Makefile.am Sun Sep 20 21:38:24 2009 +0200
5.2 +++ b/test/Makefile.am Fri Sep 25 21:51:36 2009 +0200
5.3 @@ -19,6 +19,7 @@
5.4 test/edge_set_test \
5.5 test/error_test \
5.6 test/euler_test \
5.7 + test/fractional_matching_test \
5.8 test/gomory_hu_test \
5.9 test/graph_copy_test \
5.10 test/graph_test \
5.11 @@ -65,6 +66,7 @@
5.12 test_edge_set_test_SOURCES = test/edge_set_test.cc
5.13 test_error_test_SOURCES = test/error_test.cc
5.14 test_euler_test_SOURCES = test/euler_test.cc
5.15 +test_fractional_matching_test_SOURCES = test/fractional_matching_test.cc
5.16 test_gomory_hu_test_SOURCES = test/gomory_hu_test.cc
5.17 test_graph_copy_test_SOURCES = test/graph_copy_test.cc
5.18 test_graph_test_SOURCES = test/graph_test.cc
6.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
6.2 +++ b/test/fractional_matching_test.cc Fri Sep 25 21:51:36 2009 +0200
6.3 @@ -0,0 +1,502 @@
6.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
6.5 + *
6.6 + * This file is a part of LEMON, a generic C++ optimization library.
6.7 + *
6.8 + * Copyright (C) 2003-2009
6.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
6.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
6.11 + *
6.12 + * Permission to use, modify and distribute this software is granted
6.13 + * provided that this copyright notice appears in all copies. For
6.14 + * precise terms see the accompanying LICENSE file.
6.15 + *
6.16 + * This software is provided "AS IS" with no warranty of any kind,
6.17 + * express or implied, and with no claim as to its suitability for any
6.18 + * purpose.
6.19 + *
6.20 + */
6.21 +
6.22 +#include <iostream>
6.23 +#include <sstream>
6.24 +#include <vector>
6.25 +#include <queue>
6.26 +#include <cstdlib>
6.27 +
6.28 +#include <lemon/fractional_matching.h>
6.29 +#include <lemon/smart_graph.h>
6.30 +#include <lemon/concepts/graph.h>
6.31 +#include <lemon/concepts/maps.h>
6.32 +#include <lemon/lgf_reader.h>
6.33 +#include <lemon/math.h>
6.34 +
6.35 +#include "test_tools.h"
6.36 +
6.37 +using namespace std;
6.38 +using namespace lemon;
6.39 +
6.40 +GRAPH_TYPEDEFS(SmartGraph);
6.41 +
6.42 +
6.43 +const int lgfn = 4;
6.44 +const std::string lgf[lgfn] = {
6.45 + "@nodes\n"
6.46 + "label\n"
6.47 + "0\n"
6.48 + "1\n"
6.49 + "2\n"
6.50 + "3\n"
6.51 + "4\n"
6.52 + "5\n"
6.53 + "6\n"
6.54 + "7\n"
6.55 + "@edges\n"
6.56 + " label weight\n"
6.57 + "7 4 0 984\n"
6.58 + "0 7 1 73\n"
6.59 + "7 1 2 204\n"
6.60 + "2 3 3 583\n"
6.61 + "2 7 4 565\n"
6.62 + "2 1 5 582\n"
6.63 + "0 4 6 551\n"
6.64 + "2 5 7 385\n"
6.65 + "1 5 8 561\n"
6.66 + "5 3 9 484\n"
6.67 + "7 5 10 904\n"
6.68 + "3 6 11 47\n"
6.69 + "7 6 12 888\n"
6.70 + "3 0 13 747\n"
6.71 + "6 1 14 310\n",
6.72 +
6.73 + "@nodes\n"
6.74 + "label\n"
6.75 + "0\n"
6.76 + "1\n"
6.77 + "2\n"
6.78 + "3\n"
6.79 + "4\n"
6.80 + "5\n"
6.81 + "6\n"
6.82 + "7\n"
6.83 + "@edges\n"
6.84 + " label weight\n"
6.85 + "2 5 0 710\n"
6.86 + "0 5 1 241\n"
6.87 + "2 4 2 856\n"
6.88 + "2 6 3 762\n"
6.89 + "4 1 4 747\n"
6.90 + "6 1 5 962\n"
6.91 + "4 7 6 723\n"
6.92 + "1 7 7 661\n"
6.93 + "2 3 8 376\n"
6.94 + "1 0 9 416\n"
6.95 + "6 7 10 391\n",
6.96 +
6.97 + "@nodes\n"
6.98 + "label\n"
6.99 + "0\n"
6.100 + "1\n"
6.101 + "2\n"
6.102 + "3\n"
6.103 + "4\n"
6.104 + "5\n"
6.105 + "6\n"
6.106 + "7\n"
6.107 + "@edges\n"
6.108 + " label weight\n"
6.109 + "6 2 0 553\n"
6.110 + "0 7 1 653\n"
6.111 + "6 3 2 22\n"
6.112 + "4 7 3 846\n"
6.113 + "7 2 4 981\n"
6.114 + "7 6 5 250\n"
6.115 + "5 2 6 539\n",
6.116 +
6.117 + "@nodes\n"
6.118 + "label\n"
6.119 + "0\n"
6.120 + "@edges\n"
6.121 + " label weight\n"
6.122 + "0 0 0 100\n"
6.123 +};
6.124 +
6.125 +void checkMaxFractionalMatchingCompile()
6.126 +{
6.127 + typedef concepts::Graph Graph;
6.128 + typedef Graph::Node Node;
6.129 + typedef Graph::Edge Edge;
6.130 +
6.131 + Graph g;
6.132 + Node n;
6.133 + Edge e;
6.134 +
6.135 + MaxFractionalMatching<Graph> mat_test(g);
6.136 + const MaxFractionalMatching<Graph>&
6.137 + const_mat_test = mat_test;
6.138 +
6.139 + mat_test.init();
6.140 + mat_test.start();
6.141 + mat_test.start(true);
6.142 + mat_test.startPerfect();
6.143 + mat_test.startPerfect(true);
6.144 + mat_test.run();
6.145 + mat_test.run(true);
6.146 + mat_test.runPerfect();
6.147 + mat_test.runPerfect(true);
6.148 +
6.149 + const_mat_test.matchingSize();
6.150 + const_mat_test.matching(e);
6.151 + const_mat_test.matching(n);
6.152 + const MaxFractionalMatching<Graph>::MatchingMap& mmap =
6.153 + const_mat_test.matchingMap();
6.154 + e = mmap[n];
6.155 +
6.156 + const_mat_test.barrier(n);
6.157 +}
6.158 +
6.159 +void checkMaxWeightedFractionalMatchingCompile()
6.160 +{
6.161 + typedef concepts::Graph Graph;
6.162 + typedef Graph::Node Node;
6.163 + typedef Graph::Edge Edge;
6.164 + typedef Graph::EdgeMap<int> WeightMap;
6.165 +
6.166 + Graph g;
6.167 + Node n;
6.168 + Edge e;
6.169 + WeightMap w(g);
6.170 +
6.171 + MaxWeightedFractionalMatching<Graph> mat_test(g, w);
6.172 + const MaxWeightedFractionalMatching<Graph>&
6.173 + const_mat_test = mat_test;
6.174 +
6.175 + mat_test.init();
6.176 + mat_test.start();
6.177 + mat_test.run();
6.178 +
6.179 + const_mat_test.matchingWeight();
6.180 + const_mat_test.matchingSize();
6.181 + const_mat_test.matching(e);
6.182 + const_mat_test.matching(n);
6.183 + const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap =
6.184 + const_mat_test.matchingMap();
6.185 + e = mmap[n];
6.186 +
6.187 + const_mat_test.dualValue();
6.188 + const_mat_test.nodeValue(n);
6.189 +}
6.190 +
6.191 +void checkMaxWeightedPerfectFractionalMatchingCompile()
6.192 +{
6.193 + typedef concepts::Graph Graph;
6.194 + typedef Graph::Node Node;
6.195 + typedef Graph::Edge Edge;
6.196 + typedef Graph::EdgeMap<int> WeightMap;
6.197 +
6.198 + Graph g;
6.199 + Node n;
6.200 + Edge e;
6.201 + WeightMap w(g);
6.202 +
6.203 + MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w);
6.204 + const MaxWeightedPerfectFractionalMatching<Graph>&
6.205 + const_mat_test = mat_test;
6.206 +
6.207 + mat_test.init();
6.208 + mat_test.start();
6.209 + mat_test.run();
6.210 +
6.211 + const_mat_test.matchingWeight();
6.212 + const_mat_test.matching(e);
6.213 + const_mat_test.matching(n);
6.214 + const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap =
6.215 + const_mat_test.matchingMap();
6.216 + e = mmap[n];
6.217 +
6.218 + const_mat_test.dualValue();
6.219 + const_mat_test.nodeValue(n);
6.220 +}
6.221 +
6.222 +void checkFractionalMatching(const SmartGraph& graph,
6.223 + const MaxFractionalMatching<SmartGraph>& mfm,
6.224 + bool allow_loops = true) {
6.225 + int pv = 0;
6.226 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.227 + int indeg = 0;
6.228 + for (InArcIt a(graph, n); a != INVALID; ++a) {
6.229 + if (mfm.matching(graph.source(a)) == a) {
6.230 + ++indeg;
6.231 + }
6.232 + }
6.233 + if (mfm.matching(n) != INVALID) {
6.234 + check(indeg == 1, "Invalid matching");
6.235 + ++pv;
6.236 + } else {
6.237 + check(indeg == 0, "Invalid matching");
6.238 + }
6.239 + }
6.240 + check(pv == mfm.matchingSize(), "Wrong matching size");
6.241 +
6.242 + SmartGraph::NodeMap<bool> processed(graph, false);
6.243 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.244 + if (processed[n]) continue;
6.245 + processed[n] = true;
6.246 + if (mfm.matching(n) == INVALID) continue;
6.247 + int num = 1;
6.248 + Node v = graph.target(mfm.matching(n));
6.249 + while (v != n) {
6.250 + processed[v] = true;
6.251 + ++num;
6.252 + v = graph.target(mfm.matching(v));
6.253 + }
6.254 + check(num == 2 || num % 2 == 1, "Wrong cycle size");
6.255 + check(allow_loops || num != 1, "Wrong cycle size");
6.256 + }
6.257 +
6.258 + int anum = 0, bnum = 0;
6.259 + SmartGraph::NodeMap<bool> neighbours(graph, false);
6.260 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.261 + if (!mfm.barrier(n)) continue;
6.262 + ++anum;
6.263 + for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
6.264 + Node u = graph.source(a);
6.265 + if (!allow_loops && u == n) continue;
6.266 + if (!neighbours[u]) {
6.267 + neighbours[u] = true;
6.268 + ++bnum;
6.269 + }
6.270 + }
6.271 + }
6.272 + check(anum - bnum + mfm.matchingSize() == countNodes(graph),
6.273 + "Wrong barrier");
6.274 +}
6.275 +
6.276 +void checkPerfectFractionalMatching(const SmartGraph& graph,
6.277 + const MaxFractionalMatching<SmartGraph>& mfm,
6.278 + bool perfect, bool allow_loops = true) {
6.279 + if (perfect) {
6.280 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.281 + int indeg = 0;
6.282 + for (InArcIt a(graph, n); a != INVALID; ++a) {
6.283 + if (mfm.matching(graph.source(a)) == a) {
6.284 + ++indeg;
6.285 + }
6.286 + }
6.287 + check(mfm.matching(n) != INVALID, "Invalid matching");
6.288 + check(indeg == 1, "Invalid matching");
6.289 + }
6.290 + } else {
6.291 + int anum = 0, bnum = 0;
6.292 + SmartGraph::NodeMap<bool> neighbours(graph, false);
6.293 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.294 + if (!mfm.barrier(n)) continue;
6.295 + ++anum;
6.296 + for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) {
6.297 + Node u = graph.source(a);
6.298 + if (!allow_loops && u == n) continue;
6.299 + if (!neighbours[u]) {
6.300 + neighbours[u] = true;
6.301 + ++bnum;
6.302 + }
6.303 + }
6.304 + }
6.305 + check(anum - bnum > 0, "Wrong barrier");
6.306 + }
6.307 +}
6.308 +
6.309 +void checkWeightedFractionalMatching(const SmartGraph& graph,
6.310 + const SmartGraph::EdgeMap<int>& weight,
6.311 + const MaxWeightedFractionalMatching<SmartGraph>& mwfm,
6.312 + bool allow_loops = true) {
6.313 + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
6.314 + if (graph.u(e) == graph.v(e) && !allow_loops) continue;
6.315 + int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e))
6.316 + - weight[e] * mwfm.dualScale;
6.317 +
6.318 + check(rw >= 0, "Negative reduced weight");
6.319 + check(rw == 0 || !mwfm.matching(e),
6.320 + "Non-zero reduced weight on matching edge");
6.321 + }
6.322 +
6.323 + int pv = 0;
6.324 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.325 + int indeg = 0;
6.326 + for (InArcIt a(graph, n); a != INVALID; ++a) {
6.327 + if (mwfm.matching(graph.source(a)) == a) {
6.328 + ++indeg;
6.329 + }
6.330 + }
6.331 + check(indeg <= 1, "Invalid matching");
6.332 + if (mwfm.matching(n) != INVALID) {
6.333 + check(mwfm.nodeValue(n) >= 0, "Invalid node value");
6.334 + check(indeg == 1, "Invalid matching");
6.335 + pv += weight[mwfm.matching(n)];
6.336 + SmartGraph::Node o = graph.target(mwfm.matching(n));
6.337 + } else {
6.338 + check(mwfm.nodeValue(n) == 0, "Invalid matching");
6.339 + check(indeg == 0, "Invalid matching");
6.340 + }
6.341 + }
6.342 +
6.343 + int dv = 0;
6.344 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.345 + dv += mwfm.nodeValue(n);
6.346 + }
6.347 +
6.348 + check(pv * mwfm.dualScale == dv * 2, "Wrong duality");
6.349 +
6.350 + SmartGraph::NodeMap<bool> processed(graph, false);
6.351 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.352 + if (processed[n]) continue;
6.353 + processed[n] = true;
6.354 + if (mwfm.matching(n) == INVALID) continue;
6.355 + int num = 1;
6.356 + Node v = graph.target(mwfm.matching(n));
6.357 + while (v != n) {
6.358 + processed[v] = true;
6.359 + ++num;
6.360 + v = graph.target(mwfm.matching(v));
6.361 + }
6.362 + check(num == 2 || num % 2 == 1, "Wrong cycle size");
6.363 + check(allow_loops || num != 1, "Wrong cycle size");
6.364 + }
6.365 +
6.366 + return;
6.367 +}
6.368 +
6.369 +void checkWeightedPerfectFractionalMatching(const SmartGraph& graph,
6.370 + const SmartGraph::EdgeMap<int>& weight,
6.371 + const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm,
6.372 + bool allow_loops = true) {
6.373 + for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) {
6.374 + if (graph.u(e) == graph.v(e) && !allow_loops) continue;
6.375 + int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e))
6.376 + - weight[e] * mwpfm.dualScale;
6.377 +
6.378 + check(rw >= 0, "Negative reduced weight");
6.379 + check(rw == 0 || !mwpfm.matching(e),
6.380 + "Non-zero reduced weight on matching edge");
6.381 + }
6.382 +
6.383 + int pv = 0;
6.384 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.385 + int indeg = 0;
6.386 + for (InArcIt a(graph, n); a != INVALID; ++a) {
6.387 + if (mwpfm.matching(graph.source(a)) == a) {
6.388 + ++indeg;
6.389 + }
6.390 + }
6.391 + check(mwpfm.matching(n) != INVALID, "Invalid perfect matching");
6.392 + check(indeg == 1, "Invalid perfect matching");
6.393 + pv += weight[mwpfm.matching(n)];
6.394 + SmartGraph::Node o = graph.target(mwpfm.matching(n));
6.395 + }
6.396 +
6.397 + int dv = 0;
6.398 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.399 + dv += mwpfm.nodeValue(n);
6.400 + }
6.401 +
6.402 + check(pv * mwpfm.dualScale == dv * 2, "Wrong duality");
6.403 +
6.404 + SmartGraph::NodeMap<bool> processed(graph, false);
6.405 + for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) {
6.406 + if (processed[n]) continue;
6.407 + processed[n] = true;
6.408 + if (mwpfm.matching(n) == INVALID) continue;
6.409 + int num = 1;
6.410 + Node v = graph.target(mwpfm.matching(n));
6.411 + while (v != n) {
6.412 + processed[v] = true;
6.413 + ++num;
6.414 + v = graph.target(mwpfm.matching(v));
6.415 + }
6.416 + check(num == 2 || num % 2 == 1, "Wrong cycle size");
6.417 + check(allow_loops || num != 1, "Wrong cycle size");
6.418 + }
6.419 +
6.420 + return;
6.421 +}
6.422 +
6.423 +
6.424 +int main() {
6.425 +
6.426 + for (int i = 0; i < lgfn; ++i) {
6.427 + SmartGraph graph;
6.428 + SmartGraph::EdgeMap<int> weight(graph);
6.429 +
6.430 + istringstream lgfs(lgf[i]);
6.431 + graphReader(graph, lgfs).
6.432 + edgeMap("weight", weight).run();
6.433 +
6.434 + bool perfect_with_loops;
6.435 + {
6.436 + MaxFractionalMatching<SmartGraph> mfm(graph, true);
6.437 + mfm.run();
6.438 + checkFractionalMatching(graph, mfm, true);
6.439 + perfect_with_loops = mfm.matchingSize() == countNodes(graph);
6.440 + }
6.441 +
6.442 + bool perfect_without_loops;
6.443 + {
6.444 + MaxFractionalMatching<SmartGraph> mfm(graph, false);
6.445 + mfm.run();
6.446 + checkFractionalMatching(graph, mfm, false);
6.447 + perfect_without_loops = mfm.matchingSize() == countNodes(graph);
6.448 + }
6.449 +
6.450 + {
6.451 + MaxFractionalMatching<SmartGraph> mfm(graph, true);
6.452 + bool result = mfm.runPerfect();
6.453 + checkPerfectFractionalMatching(graph, mfm, result, true);
6.454 + check(result == perfect_with_loops, "Wrong perfect matching");
6.455 + }
6.456 +
6.457 + {
6.458 + MaxFractionalMatching<SmartGraph> mfm(graph, false);
6.459 + bool result = mfm.runPerfect();
6.460 + checkPerfectFractionalMatching(graph, mfm, result, false);
6.461 + check(result == perfect_without_loops, "Wrong perfect matching");
6.462 + }
6.463 +
6.464 + {
6.465 + MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true);
6.466 + mwfm.run();
6.467 + checkWeightedFractionalMatching(graph, weight, mwfm, true);
6.468 + }
6.469 +
6.470 + {
6.471 + MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false);
6.472 + mwfm.run();
6.473 + checkWeightedFractionalMatching(graph, weight, mwfm, false);
6.474 + }
6.475 +
6.476 + {
6.477 + MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
6.478 + true);
6.479 + bool perfect = mwpfm.run();
6.480 + check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
6.481 + "Perfect matching found");
6.482 + check(perfect == perfect_with_loops, "Wrong perfect matching");
6.483 +
6.484 + if (perfect) {
6.485 + checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true);
6.486 + }
6.487 + }
6.488 +
6.489 + {
6.490 + MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight,
6.491 + false);
6.492 + bool perfect = mwpfm.run();
6.493 + check(perfect == (mwpfm.matchingSize() == countNodes(graph)),
6.494 + "Perfect matching found");
6.495 + check(perfect == perfect_without_loops, "Wrong perfect matching");
6.496 +
6.497 + if (perfect) {
6.498 + checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false);
6.499 + }
6.500 + }
6.501 +
6.502 + }
6.503 +
6.504 + return 0;
6.505 +}