3506 lines
110 KiB
C++
Executable File
3506 lines
110 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2013
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_MATCHING_H
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#define LEMON_MATCHING_H
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#include <vector>
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#include <queue>
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#include <set>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/unionfind.h>
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#include <lemon/bin_heap.h>
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#include <lemon/maps.h>
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#include <lemon/fractional_matching.h>
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///\ingroup matching
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///\file
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///\brief Maximum matching algorithms in general graphs.
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namespace lemon {
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/// \ingroup matching
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///
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/// \brief Maximum cardinality matching in general graphs
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///
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/// This class implements Edmonds' alternating forest matching algorithm
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/// for finding a maximum cardinality matching in a general undirected graph.
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/// It can be started from an arbitrary initial matching
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/// (the default is the empty one).
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///
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/// The dual solution of the problem is a map of the nodes to
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/// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),
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/// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds
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/// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph
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/// with factor-critical components, the nodes in \c ODD/A form the
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/// canonical barrier, and the nodes in \c MATCHED/C induce a graph having
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/// a perfect matching. The number of the factor-critical components
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/// minus the number of barrier nodes is a lower bound on the
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/// unmatched nodes, and the matching is optimal if and only if this bound is
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/// tight. This decomposition can be obtained using \ref status() or
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/// \ref statusMap() after running the algorithm.
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///
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/// \tparam GR The undirected graph type the algorithm runs on.
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template <typename GR>
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class MaxMatching {
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public:
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/// The graph type of the algorithm
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typedef GR Graph;
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/// The type of the matching map
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typedef typename Graph::template NodeMap<typename Graph::Arc>
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MatchingMap;
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///\brief Status constants for Gallai-Edmonds decomposition.
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///
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///These constants are used for indicating the Gallai-Edmonds
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///decomposition of a graph. The nodes with status \c EVEN (or \c D)
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///induce a subgraph with factor-critical components, the nodes with
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///status \c ODD (or \c A) form the canonical barrier, and the nodes
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///with status \c MATCHED (or \c C) induce a subgraph having a
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///perfect matching.
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enum Status {
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EVEN = 1, ///< = 1. (\c D is an alias for \c EVEN.)
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D = 1,
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MATCHED = 0, ///< = 0. (\c C is an alias for \c MATCHED.)
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C = 0,
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ODD = -1, ///< = -1. (\c A is an alias for \c ODD.)
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A = -1,
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UNMATCHED = -2 ///< = -2.
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};
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/// The type of the status map
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typedef typename Graph::template NodeMap<Status> StatusMap;
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private:
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TEMPLATE_GRAPH_TYPEDEFS(Graph);
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typedef UnionFindEnum<IntNodeMap> BlossomSet;
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typedef ExtendFindEnum<IntNodeMap> TreeSet;
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typedef RangeMap<Node> NodeIntMap;
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typedef MatchingMap EarMap;
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typedef std::vector<Node> NodeQueue;
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const Graph& _graph;
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MatchingMap* _matching;
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StatusMap* _status;
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EarMap* _ear;
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IntNodeMap* _blossom_set_index;
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BlossomSet* _blossom_set;
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NodeIntMap* _blossom_rep;
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IntNodeMap* _tree_set_index;
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TreeSet* _tree_set;
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NodeQueue _node_queue;
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int _process, _postpone, _last;
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int _node_num;
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private:
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void createStructures() {
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_node_num = countNodes(_graph);
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if (!_matching) {
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_matching = new MatchingMap(_graph);
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}
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if (!_status) {
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_status = new StatusMap(_graph);
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}
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if (!_ear) {
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_ear = new EarMap(_graph);
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}
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if (!_blossom_set) {
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_blossom_set_index = new IntNodeMap(_graph);
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_blossom_set = new BlossomSet(*_blossom_set_index);
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}
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if (!_blossom_rep) {
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_blossom_rep = new NodeIntMap(_node_num);
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}
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if (!_tree_set) {
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_tree_set_index = new IntNodeMap(_graph);
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_tree_set = new TreeSet(*_tree_set_index);
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}
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_node_queue.resize(_node_num);
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}
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void destroyStructures() {
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if (_matching) {
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delete _matching;
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}
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if (_status) {
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delete _status;
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}
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if (_ear) {
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delete _ear;
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}
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if (_blossom_set) {
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delete _blossom_set;
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delete _blossom_set_index;
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}
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if (_blossom_rep) {
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delete _blossom_rep;
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}
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if (_tree_set) {
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delete _tree_set_index;
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delete _tree_set;
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}
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}
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void processDense(const Node& n) {
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_process = _postpone = _last = 0;
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_node_queue[_last++] = n;
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while (_process != _last) {
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Node u = _node_queue[_process++];
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for (OutArcIt a(_graph, u); a != INVALID; ++a) {
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Node v = _graph.target(a);
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if ((*_status)[v] == MATCHED) {
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extendOnArc(a);
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} else if ((*_status)[v] == UNMATCHED) {
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augmentOnArc(a);
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return;
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}
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}
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}
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while (_postpone != _last) {
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Node u = _node_queue[_postpone++];
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for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
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Node v = _graph.target(a);
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if ((*_status)[v] == EVEN) {
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if (_blossom_set->find(u) != _blossom_set->find(v)) {
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shrinkOnEdge(a);
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}
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}
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while (_process != _last) {
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Node w = _node_queue[_process++];
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for (OutArcIt b(_graph, w); b != INVALID; ++b) {
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Node x = _graph.target(b);
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if ((*_status)[x] == MATCHED) {
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extendOnArc(b);
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} else if ((*_status)[x] == UNMATCHED) {
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augmentOnArc(b);
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return;
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}
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}
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}
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}
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}
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}
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void processSparse(const Node& n) {
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_process = _last = 0;
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_node_queue[_last++] = n;
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while (_process != _last) {
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Node u = _node_queue[_process++];
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for (OutArcIt a(_graph, u); a != INVALID; ++a) {
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Node v = _graph.target(a);
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if ((*_status)[v] == EVEN) {
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if (_blossom_set->find(u) != _blossom_set->find(v)) {
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shrinkOnEdge(a);
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}
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} else if ((*_status)[v] == MATCHED) {
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extendOnArc(a);
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} else if ((*_status)[v] == UNMATCHED) {
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augmentOnArc(a);
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return;
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}
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}
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}
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}
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void shrinkOnEdge(const Edge& e) {
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Node nca = INVALID;
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{
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std::set<Node> left_set, right_set;
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Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
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left_set.insert(left);
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Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
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right_set.insert(right);
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while (true) {
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if ((*_matching)[left] == INVALID) break;
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left = _graph.target((*_matching)[left]);
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left = (*_blossom_rep)[_blossom_set->
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find(_graph.target((*_ear)[left]))];
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if (right_set.find(left) != right_set.end()) {
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nca = left;
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break;
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}
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left_set.insert(left);
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if ((*_matching)[right] == INVALID) break;
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right = _graph.target((*_matching)[right]);
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right = (*_blossom_rep)[_blossom_set->
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find(_graph.target((*_ear)[right]))];
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if (left_set.find(right) != left_set.end()) {
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nca = right;
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break;
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}
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right_set.insert(right);
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}
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if (nca == INVALID) {
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if ((*_matching)[left] == INVALID) {
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nca = right;
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while (left_set.find(nca) == left_set.end()) {
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nca = _graph.target((*_matching)[nca]);
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nca =(*_blossom_rep)[_blossom_set->
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find(_graph.target((*_ear)[nca]))];
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}
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} else {
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nca = left;
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while (right_set.find(nca) == right_set.end()) {
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nca = _graph.target((*_matching)[nca]);
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nca = (*_blossom_rep)[_blossom_set->
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find(_graph.target((*_ear)[nca]))];
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}
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}
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}
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}
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{
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Node node = _graph.u(e);
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Arc arc = _graph.direct(e, true);
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Node base = (*_blossom_rep)[_blossom_set->find(node)];
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while (base != nca) {
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(*_ear)[node] = arc;
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Node n = node;
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while (n != base) {
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n = _graph.target((*_matching)[n]);
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Arc a = (*_ear)[n];
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n = _graph.target(a);
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(*_ear)[n] = _graph.oppositeArc(a);
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}
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node = _graph.target((*_matching)[base]);
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_tree_set->erase(base);
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_tree_set->erase(node);
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_blossom_set->insert(node, _blossom_set->find(base));
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(*_status)[node] = EVEN;
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_node_queue[_last++] = node;
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arc = _graph.oppositeArc((*_ear)[node]);
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node = _graph.target((*_ear)[node]);
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base = (*_blossom_rep)[_blossom_set->find(node)];
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_blossom_set->join(_graph.target(arc), base);
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}
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}
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(*_blossom_rep)[_blossom_set->find(nca)] = nca;
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{
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Node node = _graph.v(e);
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Arc arc = _graph.direct(e, false);
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Node base = (*_blossom_rep)[_blossom_set->find(node)];
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while (base != nca) {
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(*_ear)[node] = arc;
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Node n = node;
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while (n != base) {
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n = _graph.target((*_matching)[n]);
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Arc a = (*_ear)[n];
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n = _graph.target(a);
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(*_ear)[n] = _graph.oppositeArc(a);
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}
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node = _graph.target((*_matching)[base]);
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_tree_set->erase(base);
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_tree_set->erase(node);
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_blossom_set->insert(node, _blossom_set->find(base));
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(*_status)[node] = EVEN;
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_node_queue[_last++] = node;
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arc = _graph.oppositeArc((*_ear)[node]);
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node = _graph.target((*_ear)[node]);
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base = (*_blossom_rep)[_blossom_set->find(node)];
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_blossom_set->join(_graph.target(arc), base);
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}
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}
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(*_blossom_rep)[_blossom_set->find(nca)] = nca;
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}
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void extendOnArc(const Arc& a) {
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Node base = _graph.source(a);
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Node odd = _graph.target(a);
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(*_ear)[odd] = _graph.oppositeArc(a);
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Node even = _graph.target((*_matching)[odd]);
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(*_blossom_rep)[_blossom_set->insert(even)] = even;
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(*_status)[odd] = ODD;
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(*_status)[even] = EVEN;
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int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
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_tree_set->insert(odd, tree);
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_tree_set->insert(even, tree);
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_node_queue[_last++] = even;
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}
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void augmentOnArc(const Arc& a) {
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Node even = _graph.source(a);
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Node odd = _graph.target(a);
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int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
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(*_matching)[odd] = _graph.oppositeArc(a);
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(*_status)[odd] = MATCHED;
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Arc arc = (*_matching)[even];
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(*_matching)[even] = a;
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while (arc != INVALID) {
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odd = _graph.target(arc);
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arc = (*_ear)[odd];
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even = _graph.target(arc);
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(*_matching)[odd] = arc;
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arc = (*_matching)[even];
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(*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);
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}
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for (typename TreeSet::ItemIt it(*_tree_set, tree);
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it != INVALID; ++it) {
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if ((*_status)[it] == ODD) {
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(*_status)[it] = MATCHED;
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} else {
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int blossom = _blossom_set->find(it);
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for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
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jt != INVALID; ++jt) {
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(*_status)[jt] = MATCHED;
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}
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_blossom_set->eraseClass(blossom);
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}
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}
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_tree_set->eraseClass(tree);
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}
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public:
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/// \brief Constructor
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///
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/// Constructor.
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MaxMatching(const Graph& graph)
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: _graph(graph), _matching(0), _status(0), _ear(0),
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_blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
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_tree_set_index(0), _tree_set(0) {}
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~MaxMatching() {
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destroyStructures();
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}
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/// \name Execution Control
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/// The simplest way to execute the algorithm is to use the
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/// \c run() member function.\n
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/// If you need better control on the execution, you have to call
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/// one of the functions \ref init(), \ref greedyInit() or
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/// \ref matchingInit() first, then you can start the algorithm with
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/// \ref startSparse() or \ref startDense().
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///@{
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/// \brief Set the initial matching to the empty matching.
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///
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/// This function sets the initial matching to the empty matching.
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void init() {
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createStructures();
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for(NodeIt n(_graph); n != INVALID; ++n) {
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(*_matching)[n] = INVALID;
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(*_status)[n] = UNMATCHED;
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}
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}
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/// \brief Find an initial matching in a greedy way.
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///
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/// This function finds an initial matching in a greedy way.
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void greedyInit() {
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createStructures();
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for (NodeIt n(_graph); n != INVALID; ++n) {
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(*_matching)[n] = INVALID;
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(*_status)[n] = UNMATCHED;
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}
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for (NodeIt n(_graph); n != INVALID; ++n) {
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if ((*_matching)[n] == INVALID) {
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for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
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Node v = _graph.target(a);
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if ((*_matching)[v] == INVALID && v != n) {
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(*_matching)[n] = a;
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(*_status)[n] = MATCHED;
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(*_matching)[v] = _graph.oppositeArc(a);
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(*_status)[v] = MATCHED;
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break;
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}
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}
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}
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}
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}
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/// \brief Initialize the matching from a map.
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///
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/// This function initializes the matching from a \c bool valued edge
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/// map. This map should have the property that there are no two incident
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/// edges with \c true value, i.e. it really contains a matching.
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/// \return \c true if the map contains a matching.
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template <typename MatchingMap>
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bool matchingInit(const MatchingMap& matching) {
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createStructures();
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for (NodeIt n(_graph); n != INVALID; ++n) {
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(*_matching)[n] = INVALID;
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(*_status)[n] = UNMATCHED;
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}
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for(EdgeIt e(_graph); e!=INVALID; ++e) {
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if (matching[e]) {
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Node u = _graph.u(e);
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if ((*_matching)[u] != INVALID) return false;
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(*_matching)[u] = _graph.direct(e, true);
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(*_status)[u] = MATCHED;
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Node v = _graph.v(e);
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if ((*_matching)[v] != INVALID) return false;
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(*_matching)[v] = _graph.direct(e, false);
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(*_status)[v] = MATCHED;
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}
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}
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return true;
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}
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/// \brief Start Edmonds' algorithm
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///
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/// This function runs the original Edmonds' algorithm.
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///
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/// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
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/// called before using this function.
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void startSparse() {
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for(NodeIt n(_graph); n != INVALID; ++n) {
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if ((*_status)[n] == UNMATCHED) {
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(*_blossom_rep)[_blossom_set->insert(n)] = n;
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_tree_set->insert(n);
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(*_status)[n] = EVEN;
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processSparse(n);
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}
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}
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}
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|
|
|
/// \brief Start Edmonds' algorithm with a heuristic improvement
|
|
/// for dense graphs
|
|
///
|
|
/// This function runs Edmonds' algorithm with a heuristic of postponing
|
|
/// shrinks, therefore resulting in a faster algorithm for dense graphs.
|
|
///
|
|
/// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
|
|
/// called before using this function.
|
|
void startDense() {
|
|
for(NodeIt n(_graph); n != INVALID; ++n) {
|
|
if ((*_status)[n] == UNMATCHED) {
|
|
(*_blossom_rep)[_blossom_set->insert(n)] = n;
|
|
_tree_set->insert(n);
|
|
(*_status)[n] = EVEN;
|
|
processDense(n);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/// \brief Run Edmonds' algorithm
|
|
///
|
|
/// This function runs Edmonds' algorithm. An additional heuristic of
|
|
/// postponing shrinks is used for relatively dense graphs
|
|
/// (for which <tt>m>=2*n</tt> holds).
|
|
void run() {
|
|
if (countEdges(_graph) < 2 * countNodes(_graph)) {
|
|
greedyInit();
|
|
startSparse();
|
|
} else {
|
|
init();
|
|
startDense();
|
|
}
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Primal Solution
|
|
/// Functions to get the primal solution, i.e. the maximum matching.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the size (cardinality) of the matching.
|
|
///
|
|
/// This function returns the size (cardinality) of the current matching.
|
|
/// After run() it returns the size of the maximum matching in the graph.
|
|
int matchingSize() const {
|
|
int size = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if ((*_matching)[n] != INVALID) {
|
|
++size;
|
|
}
|
|
}
|
|
return size / 2;
|
|
}
|
|
|
|
/// \brief Return \c true if the given edge is in the matching.
|
|
///
|
|
/// This function returns \c true if the given edge is in the current
|
|
/// matching.
|
|
bool matching(const Edge& edge) const {
|
|
return edge == (*_matching)[_graph.u(edge)];
|
|
}
|
|
|
|
/// \brief Return the matching arc (or edge) incident to the given node.
|
|
///
|
|
/// This function returns the matching arc (or edge) incident to the
|
|
/// given node in the current matching or \c INVALID if the node is
|
|
/// not covered by the matching.
|
|
Arc matching(const Node& n) const {
|
|
return (*_matching)[n];
|
|
}
|
|
|
|
/// \brief Return a const reference to the matching map.
|
|
///
|
|
/// This function returns a const reference to a node map that stores
|
|
/// the matching arc (or edge) incident to each node.
|
|
const MatchingMap& matchingMap() const {
|
|
return *_matching;
|
|
}
|
|
|
|
/// \brief Return the mate of the given node.
|
|
///
|
|
/// This function returns the mate of the given node in the current
|
|
/// matching or \c INVALID if the node is not covered by the matching.
|
|
Node mate(const Node& n) const {
|
|
return (*_matching)[n] != INVALID ?
|
|
_graph.target((*_matching)[n]) : INVALID;
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Dual Solution
|
|
/// Functions to get the dual solution, i.e. the Gallai-Edmonds
|
|
/// decomposition.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the status of the given node in the Edmonds-Gallai
|
|
/// decomposition.
|
|
///
|
|
/// This function returns the \ref Status "status" of the given node
|
|
/// in the Edmonds-Gallai decomposition.
|
|
Status status(const Node& n) const {
|
|
return (*_status)[n];
|
|
}
|
|
|
|
/// \brief Return a const reference to the status map, which stores
|
|
/// the Edmonds-Gallai decomposition.
|
|
///
|
|
/// This function returns a const reference to a node map that stores the
|
|
/// \ref Status "status" of each node in the Edmonds-Gallai decomposition.
|
|
const StatusMap& statusMap() const {
|
|
return *_status;
|
|
}
|
|
|
|
/// \brief Return \c true if the given node is in the barrier.
|
|
///
|
|
/// This function returns \c true if the given node is in the barrier.
|
|
bool barrier(const Node& n) const {
|
|
return (*_status)[n] == ODD;
|
|
}
|
|
|
|
/// @}
|
|
|
|
};
|
|
|
|
/// \ingroup matching
|
|
///
|
|
/// \brief Weighted matching in general graphs
|
|
///
|
|
/// This class provides an efficient implementation of Edmond's
|
|
/// maximum weighted matching algorithm. The implementation is based
|
|
/// on extensive use of priority queues and provides
|
|
/// \f$O(nm\log n)\f$ time complexity.
|
|
///
|
|
/// The maximum weighted matching problem is to find a subset of the
|
|
/// edges in an undirected graph with maximum overall weight for which
|
|
/// each node has at most one incident edge.
|
|
/// It can be formulated with the following linear program.
|
|
/// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
|
|
/** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
|
|
\quad \forall B\in\mathcal{O}\f] */
|
|
/// \f[x_e \ge 0\quad \forall e\in E\f]
|
|
/// \f[\max \sum_{e\in E}x_ew_e\f]
|
|
/// where \f$\delta(X)\f$ is the set of edges incident to a node in
|
|
/// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
|
|
/// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
|
|
/// subsets of the nodes.
|
|
///
|
|
/// The algorithm calculates an optimal matching and a proof of the
|
|
/// optimality. The solution of the dual problem can be used to check
|
|
/// the result of the algorithm. The dual linear problem is the
|
|
/// following.
|
|
/** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
|
|
z_B \ge w_{uv} \quad \forall uv\in E\f] */
|
|
/// \f[y_u \ge 0 \quad \forall u \in V\f]
|
|
/// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
|
|
/** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
|
|
\frac{\vert B \vert - 1}{2}z_B\f] */
|
|
///
|
|
/// The algorithm can be executed with the run() function.
|
|
/// After it the matching (the primal solution) and the dual solution
|
|
/// can be obtained using the query functions and the
|
|
/// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class,
|
|
/// which is able to iterate on the nodes of a blossom.
|
|
/// If the value type is integer, then the dual solution is multiplied
|
|
/// by \ref MaxWeightedMatching::dualScale "4".
|
|
///
|
|
/// \tparam GR The undirected graph type the algorithm runs on.
|
|
/// \tparam WM The type edge weight map. The default type is
|
|
/// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
|
|
#ifdef DOXYGEN
|
|
template <typename GR, typename WM>
|
|
#else
|
|
template <typename GR,
|
|
typename WM = typename GR::template EdgeMap<int> >
|
|
#endif
|
|
class MaxWeightedMatching {
|
|
public:
|
|
|
|
/// The graph type of the algorithm
|
|
typedef GR Graph;
|
|
/// The type of the edge weight map
|
|
typedef WM WeightMap;
|
|
/// The value type of the edge weights
|
|
typedef typename WeightMap::Value Value;
|
|
|
|
/// The type of the matching map
|
|
typedef typename Graph::template NodeMap<typename Graph::Arc>
|
|
MatchingMap;
|
|
|
|
/// \brief Scaling factor for dual solution
|
|
///
|
|
/// Scaling factor for dual solution. It is equal to 4 or 1
|
|
/// according to the value type.
|
|
static const int dualScale =
|
|
std::numeric_limits<Value>::is_integer ? 4 : 1;
|
|
|
|
private:
|
|
|
|
TEMPLATE_GRAPH_TYPEDEFS(Graph);
|
|
|
|
typedef typename Graph::template NodeMap<Value> NodePotential;
|
|
typedef std::vector<Node> BlossomNodeList;
|
|
|
|
struct BlossomVariable {
|
|
int begin, end;
|
|
Value value;
|
|
|
|
BlossomVariable(int _begin, int _end, Value _value)
|
|
: begin(_begin), end(_end), value(_value) {}
|
|
|
|
};
|
|
|
|
typedef std::vector<BlossomVariable> BlossomPotential;
|
|
|
|
const Graph& _graph;
|
|
const WeightMap& _weight;
|
|
|
|
MatchingMap* _matching;
|
|
|
|
NodePotential* _node_potential;
|
|
|
|
BlossomPotential _blossom_potential;
|
|
BlossomNodeList _blossom_node_list;
|
|
|
|
int _node_num;
|
|
int _blossom_num;
|
|
|
|
typedef RangeMap<int> IntIntMap;
|
|
|
|
enum Status {
|
|
EVEN = -1, MATCHED = 0, ODD = 1
|
|
};
|
|
|
|
typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
|
|
struct BlossomData {
|
|
int tree;
|
|
Status status;
|
|
Arc pred, next;
|
|
Value pot, offset;
|
|
Node base;
|
|
};
|
|
|
|
IntNodeMap *_blossom_index;
|
|
BlossomSet *_blossom_set;
|
|
RangeMap<BlossomData>* _blossom_data;
|
|
|
|
IntNodeMap *_node_index;
|
|
IntArcMap *_node_heap_index;
|
|
|
|
struct NodeData {
|
|
|
|
NodeData(IntArcMap& node_heap_index)
|
|
: heap(node_heap_index) {}
|
|
|
|
int blossom;
|
|
Value pot;
|
|
BinHeap<Value, IntArcMap> heap;
|
|
std::map<int, Arc> heap_index;
|
|
|
|
int tree;
|
|
};
|
|
|
|
RangeMap<NodeData>* _node_data;
|
|
|
|
typedef ExtendFindEnum<IntIntMap> TreeSet;
|
|
|
|
IntIntMap *_tree_set_index;
|
|
TreeSet *_tree_set;
|
|
|
|
IntNodeMap *_delta1_index;
|
|
BinHeap<Value, IntNodeMap> *_delta1;
|
|
|
|
IntIntMap *_delta2_index;
|
|
BinHeap<Value, IntIntMap> *_delta2;
|
|
|
|
IntEdgeMap *_delta3_index;
|
|
BinHeap<Value, IntEdgeMap> *_delta3;
|
|
|
|
IntIntMap *_delta4_index;
|
|
BinHeap<Value, IntIntMap> *_delta4;
|
|
|
|
Value _delta_sum;
|
|
int _unmatched;
|
|
|
|
typedef MaxWeightedFractionalMatching<Graph, WeightMap> FractionalMatching;
|
|
FractionalMatching *_fractional;
|
|
|
|
void createStructures() {
|
|
_node_num = countNodes(_graph);
|
|
_blossom_num = _node_num * 3 / 2;
|
|
|
|
if (!_matching) {
|
|
_matching = new MatchingMap(_graph);
|
|
}
|
|
|
|
if (!_node_potential) {
|
|
_node_potential = new NodePotential(_graph);
|
|
}
|
|
|
|
if (!_blossom_set) {
|
|
_blossom_index = new IntNodeMap(_graph);
|
|
_blossom_set = new BlossomSet(*_blossom_index);
|
|
_blossom_data = new RangeMap<BlossomData>(_blossom_num);
|
|
} else if (_blossom_data->size() != _blossom_num) {
|
|
delete _blossom_data;
|
|
_blossom_data = new RangeMap<BlossomData>(_blossom_num);
|
|
}
|
|
|
|
if (!_node_index) {
|
|
_node_index = new IntNodeMap(_graph);
|
|
_node_heap_index = new IntArcMap(_graph);
|
|
_node_data = new RangeMap<NodeData>(_node_num,
|
|
NodeData(*_node_heap_index));
|
|
} else {
|
|
delete _node_data;
|
|
_node_data = new RangeMap<NodeData>(_node_num,
|
|
NodeData(*_node_heap_index));
|
|
}
|
|
|
|
if (!_tree_set) {
|
|
_tree_set_index = new IntIntMap(_blossom_num);
|
|
_tree_set = new TreeSet(*_tree_set_index);
|
|
} else {
|
|
_tree_set_index->resize(_blossom_num);
|
|
}
|
|
|
|
if (!_delta1) {
|
|
_delta1_index = new IntNodeMap(_graph);
|
|
_delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
|
|
}
|
|
|
|
if (!_delta2) {
|
|
_delta2_index = new IntIntMap(_blossom_num);
|
|
_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
|
|
} else {
|
|
_delta2_index->resize(_blossom_num);
|
|
}
|
|
|
|
if (!_delta3) {
|
|
_delta3_index = new IntEdgeMap(_graph);
|
|
_delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
|
|
}
|
|
|
|
if (!_delta4) {
|
|
_delta4_index = new IntIntMap(_blossom_num);
|
|
_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
|
|
} else {
|
|
_delta4_index->resize(_blossom_num);
|
|
}
|
|
}
|
|
|
|
void destroyStructures() {
|
|
if (_matching) {
|
|
delete _matching;
|
|
}
|
|
if (_node_potential) {
|
|
delete _node_potential;
|
|
}
|
|
if (_blossom_set) {
|
|
delete _blossom_index;
|
|
delete _blossom_set;
|
|
delete _blossom_data;
|
|
}
|
|
|
|
if (_node_index) {
|
|
delete _node_index;
|
|
delete _node_heap_index;
|
|
delete _node_data;
|
|
}
|
|
|
|
if (_tree_set) {
|
|
delete _tree_set_index;
|
|
delete _tree_set;
|
|
}
|
|
if (_delta1) {
|
|
delete _delta1_index;
|
|
delete _delta1;
|
|
}
|
|
if (_delta2) {
|
|
delete _delta2_index;
|
|
delete _delta2;
|
|
}
|
|
if (_delta3) {
|
|
delete _delta3_index;
|
|
delete _delta3;
|
|
}
|
|
if (_delta4) {
|
|
delete _delta4_index;
|
|
delete _delta4;
|
|
}
|
|
}
|
|
|
|
void matchedToEven(int blossom, int tree) {
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
(*_blossom_data)[blossom].pot -=
|
|
2 * (_delta_sum - (*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
|
|
_blossom_set->increase(n, std::numeric_limits<Value>::max());
|
|
int ni = (*_node_index)[n];
|
|
|
|
(*_node_data)[ni].heap.clear();
|
|
(*_node_data)[ni].heap_index.clear();
|
|
|
|
(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
|
|
|
|
_delta1->push(n, (*_node_data)[ni].pot);
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
|
|
_delta3->push(e, rw / 2);
|
|
}
|
|
} else {
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
if ((*_node_data)[vi].heap[it->second] > rw) {
|
|
(*_node_data)[vi].heap.replace(it->second, e);
|
|
(*_node_data)[vi].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[vi].heap.push(e, rw);
|
|
(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
|
|
}
|
|
|
|
if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_delta2->state(vb) != _delta2->IN_HEAP) {
|
|
_delta2->push(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset) {
|
|
_delta2->decrease(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
}
|
|
|
|
void matchedToOdd(int blossom) {
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
(*_blossom_data)[blossom].offset += _delta_sum;
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
}
|
|
|
|
void evenToMatched(int blossom, int tree) {
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
(*_blossom_data)[blossom].pot += 2 * _delta_sum;
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
int ni = (*_node_index)[n];
|
|
(*_node_data)[ni].pot -= _delta_sum;
|
|
|
|
_delta1->erase(n);
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if (vb == blossom) {
|
|
if (_delta3->state(e) == _delta3->IN_HEAP) {
|
|
_delta3->erase(e);
|
|
}
|
|
} else if ((*_blossom_data)[vb].status == EVEN) {
|
|
|
|
if (_delta3->state(e) == _delta3->IN_HEAP) {
|
|
_delta3->erase(e);
|
|
}
|
|
|
|
int vt = _tree_set->find(vb);
|
|
|
|
if (vt != tree) {
|
|
|
|
Arc r = _graph.oppositeArc(e);
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[ni].heap_index.find(vt);
|
|
|
|
if (it != (*_node_data)[ni].heap_index.end()) {
|
|
if ((*_node_data)[ni].heap[it->second] > rw) {
|
|
(*_node_data)[ni].heap.replace(it->second, r);
|
|
(*_node_data)[ni].heap.decrease(r, rw);
|
|
it->second = r;
|
|
}
|
|
} else {
|
|
(*_node_data)[ni].heap.push(r, rw);
|
|
(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
|
|
}
|
|
|
|
if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
|
|
_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
|
|
|
|
if (_delta2->state(blossom) != _delta2->IN_HEAP) {
|
|
_delta2->push(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
} else if ((*_delta2)[blossom] >
|
|
_blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset){
|
|
_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
(*_node_data)[vi].heap.erase(it->second);
|
|
(*_node_data)[vi].heap_index.erase(it);
|
|
if ((*_node_data)[vi].heap.empty()) {
|
|
_blossom_set->increase(v, std::numeric_limits<Value>::max());
|
|
} else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
|
|
}
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_blossom_set->classPrio(vb) ==
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->erase(vb);
|
|
} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset) {
|
|
_delta2->increase(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void oddToMatched(int blossom) {
|
|
(*_blossom_data)[blossom].offset -= _delta_sum;
|
|
|
|
if (_blossom_set->classPrio(blossom) !=
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->push(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->erase(blossom);
|
|
}
|
|
}
|
|
|
|
void oddToEven(int blossom, int tree) {
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->erase(blossom);
|
|
(*_blossom_data)[blossom].pot -=
|
|
2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
int ni = (*_node_index)[n];
|
|
|
|
_blossom_set->increase(n, std::numeric_limits<Value>::max());
|
|
|
|
(*_node_data)[ni].heap.clear();
|
|
(*_node_data)[ni].heap_index.clear();
|
|
(*_node_data)[ni].pot +=
|
|
2 * _delta_sum - (*_blossom_data)[blossom].offset;
|
|
|
|
_delta1->push(n, (*_node_data)[ni].pot);
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
|
|
_delta3->push(e, rw / 2);
|
|
}
|
|
} else {
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
if ((*_node_data)[vi].heap[it->second] > rw) {
|
|
(*_node_data)[vi].heap.replace(it->second, e);
|
|
(*_node_data)[vi].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[vi].heap.push(e, rw);
|
|
(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
|
|
}
|
|
|
|
if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_delta2->state(vb) != _delta2->IN_HEAP) {
|
|
_delta2->push(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset) {
|
|
_delta2->decrease(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
}
|
|
|
|
void alternatePath(int even, int tree) {
|
|
int odd;
|
|
|
|
evenToMatched(even, tree);
|
|
(*_blossom_data)[even].status = MATCHED;
|
|
|
|
while ((*_blossom_data)[even].pred != INVALID) {
|
|
odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
|
|
(*_blossom_data)[odd].status = MATCHED;
|
|
oddToMatched(odd);
|
|
(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
|
|
|
|
even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
|
|
(*_blossom_data)[even].status = MATCHED;
|
|
evenToMatched(even, tree);
|
|
(*_blossom_data)[even].next =
|
|
_graph.oppositeArc((*_blossom_data)[odd].pred);
|
|
}
|
|
|
|
}
|
|
|
|
void destroyTree(int tree) {
|
|
for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
|
|
if ((*_blossom_data)[b].status == EVEN) {
|
|
(*_blossom_data)[b].status = MATCHED;
|
|
evenToMatched(b, tree);
|
|
} else if ((*_blossom_data)[b].status == ODD) {
|
|
(*_blossom_data)[b].status = MATCHED;
|
|
oddToMatched(b);
|
|
}
|
|
}
|
|
_tree_set->eraseClass(tree);
|
|
}
|
|
|
|
|
|
void unmatchNode(const Node& node) {
|
|
int blossom = _blossom_set->find(node);
|
|
int tree = _tree_set->find(blossom);
|
|
|
|
alternatePath(blossom, tree);
|
|
destroyTree(tree);
|
|
|
|
(*_blossom_data)[blossom].base = node;
|
|
(*_blossom_data)[blossom].next = INVALID;
|
|
}
|
|
|
|
void augmentOnEdge(const Edge& edge) {
|
|
|
|
int left = _blossom_set->find(_graph.u(edge));
|
|
int right = _blossom_set->find(_graph.v(edge));
|
|
|
|
int left_tree = _tree_set->find(left);
|
|
alternatePath(left, left_tree);
|
|
destroyTree(left_tree);
|
|
|
|
int right_tree = _tree_set->find(right);
|
|
alternatePath(right, right_tree);
|
|
destroyTree(right_tree);
|
|
|
|
(*_blossom_data)[left].next = _graph.direct(edge, true);
|
|
(*_blossom_data)[right].next = _graph.direct(edge, false);
|
|
}
|
|
|
|
void augmentOnArc(const Arc& arc) {
|
|
|
|
int left = _blossom_set->find(_graph.source(arc));
|
|
int right = _blossom_set->find(_graph.target(arc));
|
|
|
|
(*_blossom_data)[left].status = MATCHED;
|
|
|
|
int right_tree = _tree_set->find(right);
|
|
alternatePath(right, right_tree);
|
|
destroyTree(right_tree);
|
|
|
|
(*_blossom_data)[left].next = arc;
|
|
(*_blossom_data)[right].next = _graph.oppositeArc(arc);
|
|
}
|
|
|
|
void extendOnArc(const Arc& arc) {
|
|
int base = _blossom_set->find(_graph.target(arc));
|
|
int tree = _tree_set->find(base);
|
|
|
|
int odd = _blossom_set->find(_graph.source(arc));
|
|
_tree_set->insert(odd, tree);
|
|
(*_blossom_data)[odd].status = ODD;
|
|
matchedToOdd(odd);
|
|
(*_blossom_data)[odd].pred = arc;
|
|
|
|
int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
|
|
(*_blossom_data)[even].pred = (*_blossom_data)[even].next;
|
|
_tree_set->insert(even, tree);
|
|
(*_blossom_data)[even].status = EVEN;
|
|
matchedToEven(even, tree);
|
|
}
|
|
|
|
void shrinkOnEdge(const Edge& edge, int tree) {
|
|
int nca = -1;
|
|
std::vector<int> left_path, right_path;
|
|
|
|
{
|
|
std::set<int> left_set, right_set;
|
|
int left = _blossom_set->find(_graph.u(edge));
|
|
left_path.push_back(left);
|
|
left_set.insert(left);
|
|
|
|
int right = _blossom_set->find(_graph.v(edge));
|
|
right_path.push_back(right);
|
|
right_set.insert(right);
|
|
|
|
while (true) {
|
|
|
|
if ((*_blossom_data)[left].pred == INVALID) break;
|
|
|
|
left =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
|
|
left_path.push_back(left);
|
|
left =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
|
|
left_path.push_back(left);
|
|
|
|
left_set.insert(left);
|
|
|
|
if (right_set.find(left) != right_set.end()) {
|
|
nca = left;
|
|
break;
|
|
}
|
|
|
|
if ((*_blossom_data)[right].pred == INVALID) break;
|
|
|
|
right =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
|
|
right_path.push_back(right);
|
|
right =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
|
|
right_path.push_back(right);
|
|
|
|
right_set.insert(right);
|
|
|
|
if (left_set.find(right) != left_set.end()) {
|
|
nca = right;
|
|
break;
|
|
}
|
|
|
|
}
|
|
|
|
if (nca == -1) {
|
|
if ((*_blossom_data)[left].pred == INVALID) {
|
|
nca = right;
|
|
while (left_set.find(nca) == left_set.end()) {
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
right_path.push_back(nca);
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
right_path.push_back(nca);
|
|
}
|
|
} else {
|
|
nca = left;
|
|
while (right_set.find(nca) == right_set.end()) {
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
left_path.push_back(nca);
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
left_path.push_back(nca);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
std::vector<int> subblossoms;
|
|
Arc prev;
|
|
|
|
prev = _graph.direct(edge, true);
|
|
for (int i = 0; left_path[i] != nca; i += 2) {
|
|
subblossoms.push_back(left_path[i]);
|
|
(*_blossom_data)[left_path[i]].next = prev;
|
|
_tree_set->erase(left_path[i]);
|
|
|
|
subblossoms.push_back(left_path[i + 1]);
|
|
(*_blossom_data)[left_path[i + 1]].status = EVEN;
|
|
oddToEven(left_path[i + 1], tree);
|
|
_tree_set->erase(left_path[i + 1]);
|
|
prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
|
|
}
|
|
|
|
int k = 0;
|
|
while (right_path[k] != nca) ++k;
|
|
|
|
subblossoms.push_back(nca);
|
|
(*_blossom_data)[nca].next = prev;
|
|
|
|
for (int i = k - 2; i >= 0; i -= 2) {
|
|
subblossoms.push_back(right_path[i + 1]);
|
|
(*_blossom_data)[right_path[i + 1]].status = EVEN;
|
|
oddToEven(right_path[i + 1], tree);
|
|
_tree_set->erase(right_path[i + 1]);
|
|
|
|
(*_blossom_data)[right_path[i + 1]].next =
|
|
(*_blossom_data)[right_path[i + 1]].pred;
|
|
|
|
subblossoms.push_back(right_path[i]);
|
|
_tree_set->erase(right_path[i]);
|
|
}
|
|
|
|
int surface =
|
|
_blossom_set->join(subblossoms.begin(), subblossoms.end());
|
|
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (!_blossom_set->trivial(subblossoms[i])) {
|
|
(*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
|
|
}
|
|
(*_blossom_data)[subblossoms[i]].status = MATCHED;
|
|
}
|
|
|
|
(*_blossom_data)[surface].pot = -2 * _delta_sum;
|
|
(*_blossom_data)[surface].offset = 0;
|
|
(*_blossom_data)[surface].status = EVEN;
|
|
(*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
|
|
(*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
|
|
|
|
_tree_set->insert(surface, tree);
|
|
_tree_set->erase(nca);
|
|
}
|
|
|
|
void splitBlossom(int blossom) {
|
|
Arc next = (*_blossom_data)[blossom].next;
|
|
Arc pred = (*_blossom_data)[blossom].pred;
|
|
|
|
int tree = _tree_set->find(blossom);
|
|
|
|
(*_blossom_data)[blossom].status = MATCHED;
|
|
oddToMatched(blossom);
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
|
|
std::vector<int> subblossoms;
|
|
_blossom_set->split(blossom, std::back_inserter(subblossoms));
|
|
|
|
Value offset = (*_blossom_data)[blossom].offset;
|
|
int b = _blossom_set->find(_graph.source(pred));
|
|
int d = _blossom_set->find(_graph.source(next));
|
|
|
|
int ib = -1, id = -1;
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (subblossoms[i] == b) ib = i;
|
|
if (subblossoms[i] == d) id = i;
|
|
|
|
(*_blossom_data)[subblossoms[i]].offset = offset;
|
|
if (!_blossom_set->trivial(subblossoms[i])) {
|
|
(*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
|
|
}
|
|
if (_blossom_set->classPrio(subblossoms[i]) !=
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->push(subblossoms[i],
|
|
_blossom_set->classPrio(subblossoms[i]) -
|
|
(*_blossom_data)[subblossoms[i]].offset);
|
|
}
|
|
}
|
|
|
|
if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
|
|
for (int i = (id + 1) % subblossoms.size();
|
|
i != ib; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
}
|
|
|
|
for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
int ub = subblossoms[(i + 2) % subblossoms.size()];
|
|
|
|
(*_blossom_data)[sb].status = ODD;
|
|
matchedToOdd(sb);
|
|
_tree_set->insert(sb, tree);
|
|
(*_blossom_data)[sb].pred = pred;
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
|
|
pred = (*_blossom_data)[ub].next;
|
|
|
|
(*_blossom_data)[tb].status = EVEN;
|
|
matchedToEven(tb, tree);
|
|
_tree_set->insert(tb, tree);
|
|
(*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
|
|
}
|
|
|
|
(*_blossom_data)[subblossoms[id]].status = ODD;
|
|
matchedToOdd(subblossoms[id]);
|
|
_tree_set->insert(subblossoms[id], tree);
|
|
(*_blossom_data)[subblossoms[id]].next = next;
|
|
(*_blossom_data)[subblossoms[id]].pred = pred;
|
|
|
|
} else {
|
|
|
|
for (int i = (ib + 1) % subblossoms.size();
|
|
i != id; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
}
|
|
|
|
for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
int ub = subblossoms[(i + 2) % subblossoms.size()];
|
|
|
|
(*_blossom_data)[sb].status = ODD;
|
|
matchedToOdd(sb);
|
|
_tree_set->insert(sb, tree);
|
|
(*_blossom_data)[sb].next = next;
|
|
(*_blossom_data)[sb].pred =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
|
|
(*_blossom_data)[tb].status = EVEN;
|
|
matchedToEven(tb, tree);
|
|
_tree_set->insert(tb, tree);
|
|
(*_blossom_data)[tb].pred =
|
|
(*_blossom_data)[tb].next =
|
|
_graph.oppositeArc((*_blossom_data)[ub].next);
|
|
next = (*_blossom_data)[ub].next;
|
|
}
|
|
|
|
(*_blossom_data)[subblossoms[ib]].status = ODD;
|
|
matchedToOdd(subblossoms[ib]);
|
|
_tree_set->insert(subblossoms[ib], tree);
|
|
(*_blossom_data)[subblossoms[ib]].next = next;
|
|
(*_blossom_data)[subblossoms[ib]].pred = pred;
|
|
}
|
|
_tree_set->erase(blossom);
|
|
}
|
|
|
|
void extractBlossom(int blossom, const Node& base, const Arc& matching) {
|
|
if (_blossom_set->trivial(blossom)) {
|
|
int bi = (*_node_index)[base];
|
|
Value pot = (*_node_data)[bi].pot;
|
|
|
|
(*_matching)[base] = matching;
|
|
_blossom_node_list.push_back(base);
|
|
(*_node_potential)[base] = pot;
|
|
} else {
|
|
|
|
Value pot = (*_blossom_data)[blossom].pot;
|
|
int bn = _blossom_node_list.size();
|
|
|
|
std::vector<int> subblossoms;
|
|
_blossom_set->split(blossom, std::back_inserter(subblossoms));
|
|
int b = _blossom_set->find(base);
|
|
int ib = -1;
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (subblossoms[i] == b) { ib = i; break; }
|
|
}
|
|
|
|
for (int i = 1; i < int(subblossoms.size()); i += 2) {
|
|
int sb = subblossoms[(ib + i) % subblossoms.size()];
|
|
int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
|
|
|
|
Arc m = (*_blossom_data)[tb].next;
|
|
extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
|
|
extractBlossom(tb, _graph.source(m), m);
|
|
}
|
|
extractBlossom(subblossoms[ib], base, matching);
|
|
|
|
int en = _blossom_node_list.size();
|
|
|
|
_blossom_potential.push_back(BlossomVariable(bn, en, pot));
|
|
}
|
|
}
|
|
|
|
void extractMatching() {
|
|
std::vector<int> blossoms;
|
|
for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
|
|
blossoms.push_back(c);
|
|
}
|
|
|
|
for (int i = 0; i < int(blossoms.size()); ++i) {
|
|
if ((*_blossom_data)[blossoms[i]].next != INVALID) {
|
|
|
|
Value offset = (*_blossom_data)[blossoms[i]].offset;
|
|
(*_blossom_data)[blossoms[i]].pot += 2 * offset;
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
|
|
n != INVALID; ++n) {
|
|
(*_node_data)[(*_node_index)[n]].pot -= offset;
|
|
}
|
|
|
|
Arc matching = (*_blossom_data)[blossoms[i]].next;
|
|
Node base = _graph.source(matching);
|
|
extractBlossom(blossoms[i], base, matching);
|
|
} else {
|
|
Node base = (*_blossom_data)[blossoms[i]].base;
|
|
extractBlossom(blossoms[i], base, INVALID);
|
|
}
|
|
}
|
|
}
|
|
|
|
public:
|
|
|
|
/// \brief Constructor
|
|
///
|
|
/// Constructor.
|
|
MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
|
|
: _graph(graph), _weight(weight), _matching(0),
|
|
_node_potential(0), _blossom_potential(), _blossom_node_list(),
|
|
_node_num(0), _blossom_num(0),
|
|
|
|
_blossom_index(0), _blossom_set(0), _blossom_data(0),
|
|
_node_index(0), _node_heap_index(0), _node_data(0),
|
|
_tree_set_index(0), _tree_set(0),
|
|
|
|
_delta1_index(0), _delta1(0),
|
|
_delta2_index(0), _delta2(0),
|
|
_delta3_index(0), _delta3(0),
|
|
_delta4_index(0), _delta4(0),
|
|
|
|
_delta_sum(), _unmatched(0),
|
|
|
|
_fractional(0)
|
|
{}
|
|
|
|
~MaxWeightedMatching() {
|
|
destroyStructures();
|
|
if (_fractional) {
|
|
delete _fractional;
|
|
}
|
|
}
|
|
|
|
/// \name Execution Control
|
|
/// The simplest way to execute the algorithm is to use the
|
|
/// \ref run() member function.
|
|
|
|
///@{
|
|
|
|
/// \brief Initialize the algorithm
|
|
///
|
|
/// This function initializes the algorithm.
|
|
void init() {
|
|
createStructures();
|
|
|
|
_blossom_node_list.clear();
|
|
_blossom_potential.clear();
|
|
|
|
for (ArcIt e(_graph); e != INVALID; ++e) {
|
|
(*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
|
|
}
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
(*_delta1_index)[n] = _delta1->PRE_HEAP;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
(*_delta3_index)[e] = _delta3->PRE_HEAP;
|
|
}
|
|
for (int i = 0; i < _blossom_num; ++i) {
|
|
(*_delta2_index)[i] = _delta2->PRE_HEAP;
|
|
(*_delta4_index)[i] = _delta4->PRE_HEAP;
|
|
}
|
|
|
|
_unmatched = _node_num;
|
|
|
|
_delta1->clear();
|
|
_delta2->clear();
|
|
_delta3->clear();
|
|
_delta4->clear();
|
|
_blossom_set->clear();
|
|
_tree_set->clear();
|
|
|
|
int index = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
Value max = 0;
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
if (_graph.target(e) == n) continue;
|
|
if ((dualScale * _weight[e]) / 2 > max) {
|
|
max = (dualScale * _weight[e]) / 2;
|
|
}
|
|
}
|
|
(*_node_index)[n] = index;
|
|
(*_node_data)[index].heap_index.clear();
|
|
(*_node_data)[index].heap.clear();
|
|
(*_node_data)[index].pot = max;
|
|
_delta1->push(n, max);
|
|
int blossom =
|
|
_blossom_set->insert(n, std::numeric_limits<Value>::max());
|
|
|
|
_tree_set->insert(blossom);
|
|
|
|
(*_blossom_data)[blossom].status = EVEN;
|
|
(*_blossom_data)[blossom].pred = INVALID;
|
|
(*_blossom_data)[blossom].next = INVALID;
|
|
(*_blossom_data)[blossom].pot = 0;
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
++index;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
int si = (*_node_index)[_graph.u(e)];
|
|
int ti = (*_node_index)[_graph.v(e)];
|
|
if (_graph.u(e) != _graph.v(e)) {
|
|
_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
|
|
dualScale * _weight[e]) / 2);
|
|
}
|
|
}
|
|
}
|
|
|
|
/// \brief Initialize the algorithm with fractional matching
|
|
///
|
|
/// This function initializes the algorithm with a fractional
|
|
/// matching. This initialization is also called jumpstart heuristic.
|
|
void fractionalInit() {
|
|
createStructures();
|
|
|
|
_blossom_node_list.clear();
|
|
_blossom_potential.clear();
|
|
|
|
if (_fractional == 0) {
|
|
_fractional = new FractionalMatching(_graph, _weight, false);
|
|
}
|
|
_fractional->run();
|
|
|
|
for (ArcIt e(_graph); e != INVALID; ++e) {
|
|
(*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
|
|
}
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
(*_delta1_index)[n] = _delta1->PRE_HEAP;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
(*_delta3_index)[e] = _delta3->PRE_HEAP;
|
|
}
|
|
for (int i = 0; i < _blossom_num; ++i) {
|
|
(*_delta2_index)[i] = _delta2->PRE_HEAP;
|
|
(*_delta4_index)[i] = _delta4->PRE_HEAP;
|
|
}
|
|
|
|
_unmatched = 0;
|
|
|
|
_delta1->clear();
|
|
_delta2->clear();
|
|
_delta3->clear();
|
|
_delta4->clear();
|
|
_blossom_set->clear();
|
|
_tree_set->clear();
|
|
|
|
int index = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
Value pot = _fractional->nodeValue(n);
|
|
(*_node_index)[n] = index;
|
|
(*_node_data)[index].pot = pot;
|
|
(*_node_data)[index].heap_index.clear();
|
|
(*_node_data)[index].heap.clear();
|
|
int blossom =
|
|
_blossom_set->insert(n, std::numeric_limits<Value>::max());
|
|
|
|
(*_blossom_data)[blossom].status = MATCHED;
|
|
(*_blossom_data)[blossom].pred = INVALID;
|
|
(*_blossom_data)[blossom].next = _fractional->matching(n);
|
|
if (_fractional->matching(n) == INVALID) {
|
|
(*_blossom_data)[blossom].base = n;
|
|
}
|
|
(*_blossom_data)[blossom].pot = 0;
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
++index;
|
|
}
|
|
|
|
typename Graph::template NodeMap<bool> processed(_graph, false);
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if (processed[n]) continue;
|
|
processed[n] = true;
|
|
if (_fractional->matching(n) == INVALID) continue;
|
|
int num = 1;
|
|
Node v = _graph.target(_fractional->matching(n));
|
|
while (n != v) {
|
|
processed[v] = true;
|
|
v = _graph.target(_fractional->matching(v));
|
|
++num;
|
|
}
|
|
|
|
if (num % 2 == 1) {
|
|
std::vector<int> subblossoms(num);
|
|
|
|
subblossoms[--num] = _blossom_set->find(n);
|
|
_delta1->push(n, _fractional->nodeValue(n));
|
|
v = _graph.target(_fractional->matching(n));
|
|
while (n != v) {
|
|
subblossoms[--num] = _blossom_set->find(v);
|
|
_delta1->push(v, _fractional->nodeValue(v));
|
|
v = _graph.target(_fractional->matching(v));
|
|
}
|
|
|
|
int surface =
|
|
_blossom_set->join(subblossoms.begin(), subblossoms.end());
|
|
(*_blossom_data)[surface].status = EVEN;
|
|
(*_blossom_data)[surface].pred = INVALID;
|
|
(*_blossom_data)[surface].next = INVALID;
|
|
(*_blossom_data)[surface].pot = 0;
|
|
(*_blossom_data)[surface].offset = 0;
|
|
|
|
_tree_set->insert(surface);
|
|
++_unmatched;
|
|
}
|
|
}
|
|
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
int si = (*_node_index)[_graph.u(e)];
|
|
int sb = _blossom_set->find(_graph.u(e));
|
|
int ti = (*_node_index)[_graph.v(e)];
|
|
int tb = _blossom_set->find(_graph.v(e));
|
|
if ((*_blossom_data)[sb].status == EVEN &&
|
|
(*_blossom_data)[tb].status == EVEN && sb != tb) {
|
|
_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
|
|
dualScale * _weight[e]) / 2);
|
|
}
|
|
}
|
|
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
int nb = _blossom_set->find(n);
|
|
if ((*_blossom_data)[nb].status != MATCHED) continue;
|
|
int ni = (*_node_index)[n];
|
|
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.target(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
|
|
int vt = _tree_set->find(vb);
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[ni].heap_index.find(vt);
|
|
|
|
if (it != (*_node_data)[ni].heap_index.end()) {
|
|
if ((*_node_data)[ni].heap[it->second] > rw) {
|
|
(*_node_data)[ni].heap.replace(it->second, e);
|
|
(*_node_data)[ni].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[ni].heap.push(e, rw);
|
|
(*_node_data)[ni].heap_index.insert(std::make_pair(vt, e));
|
|
}
|
|
}
|
|
}
|
|
|
|
if (!(*_node_data)[ni].heap.empty()) {
|
|
_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
|
|
_delta2->push(nb, _blossom_set->classPrio(nb));
|
|
}
|
|
}
|
|
}
|
|
|
|
/// \brief Start the algorithm
|
|
///
|
|
/// This function starts the algorithm.
|
|
///
|
|
/// \pre \ref init() or \ref fractionalInit() must be called
|
|
/// before using this function.
|
|
void start() {
|
|
enum OpType {
|
|
D1, D2, D3, D4
|
|
};
|
|
|
|
while (_unmatched > 0) {
|
|
Value d1 = !_delta1->empty() ?
|
|
_delta1->prio() : std::numeric_limits<Value>::max();
|
|
|
|
Value d2 = !_delta2->empty() ?
|
|
_delta2->prio() : std::numeric_limits<Value>::max();
|
|
|
|
Value d3 = !_delta3->empty() ?
|
|
_delta3->prio() : std::numeric_limits<Value>::max();
|
|
|
|
Value d4 = !_delta4->empty() ?
|
|
_delta4->prio() : std::numeric_limits<Value>::max();
|
|
|
|
_delta_sum = d3; OpType ot = D3;
|
|
if (d1 < _delta_sum) { _delta_sum = d1; ot = D1; }
|
|
if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
|
|
if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
|
|
|
|
switch (ot) {
|
|
case D1:
|
|
{
|
|
Node n = _delta1->top();
|
|
unmatchNode(n);
|
|
--_unmatched;
|
|
}
|
|
break;
|
|
case D2:
|
|
{
|
|
int blossom = _delta2->top();
|
|
Node n = _blossom_set->classTop(blossom);
|
|
Arc a = (*_node_data)[(*_node_index)[n]].heap.top();
|
|
if ((*_blossom_data)[blossom].next == INVALID) {
|
|
augmentOnArc(a);
|
|
--_unmatched;
|
|
} else {
|
|
extendOnArc(a);
|
|
}
|
|
}
|
|
break;
|
|
case D3:
|
|
{
|
|
Edge e = _delta3->top();
|
|
|
|
int left_blossom = _blossom_set->find(_graph.u(e));
|
|
int right_blossom = _blossom_set->find(_graph.v(e));
|
|
|
|
if (left_blossom == right_blossom) {
|
|
_delta3->pop();
|
|
} else {
|
|
int left_tree = _tree_set->find(left_blossom);
|
|
int right_tree = _tree_set->find(right_blossom);
|
|
|
|
if (left_tree == right_tree) {
|
|
shrinkOnEdge(e, left_tree);
|
|
} else {
|
|
augmentOnEdge(e);
|
|
_unmatched -= 2;
|
|
}
|
|
}
|
|
} break;
|
|
case D4:
|
|
splitBlossom(_delta4->top());
|
|
break;
|
|
}
|
|
}
|
|
extractMatching();
|
|
}
|
|
|
|
/// \brief Run the algorithm.
|
|
///
|
|
/// This method runs the \c %MaxWeightedMatching algorithm.
|
|
///
|
|
/// \note mwm.run() is just a shortcut of the following code.
|
|
/// \code
|
|
/// mwm.fractionalInit();
|
|
/// mwm.start();
|
|
/// \endcode
|
|
void run() {
|
|
fractionalInit();
|
|
start();
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Primal Solution
|
|
/// Functions to get the primal solution, i.e. the maximum weighted
|
|
/// matching.\n
|
|
/// Either \ref run() or \ref start() function should be called before
|
|
/// using them.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the weight of the matching.
|
|
///
|
|
/// This function returns the weight of the found matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value matchingWeight() const {
|
|
Value sum = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if ((*_matching)[n] != INVALID) {
|
|
sum += _weight[(*_matching)[n]];
|
|
}
|
|
}
|
|
return sum / 2;
|
|
}
|
|
|
|
/// \brief Return the size (cardinality) of the matching.
|
|
///
|
|
/// This function returns the size (cardinality) of the found matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
int matchingSize() const {
|
|
int num = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if ((*_matching)[n] != INVALID) {
|
|
++num;
|
|
}
|
|
}
|
|
return num /= 2;
|
|
}
|
|
|
|
/// \brief Return \c true if the given edge is in the matching.
|
|
///
|
|
/// This function returns \c true if the given edge is in the found
|
|
/// matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
bool matching(const Edge& edge) const {
|
|
return edge == (*_matching)[_graph.u(edge)];
|
|
}
|
|
|
|
/// \brief Return the matching arc (or edge) incident to the given node.
|
|
///
|
|
/// This function returns the matching arc (or edge) incident to the
|
|
/// given node in the found matching or \c INVALID if the node is
|
|
/// not covered by the matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Arc matching(const Node& node) const {
|
|
return (*_matching)[node];
|
|
}
|
|
|
|
/// \brief Return a const reference to the matching map.
|
|
///
|
|
/// This function returns a const reference to a node map that stores
|
|
/// the matching arc (or edge) incident to each node.
|
|
const MatchingMap& matchingMap() const {
|
|
return *_matching;
|
|
}
|
|
|
|
/// \brief Return the mate of the given node.
|
|
///
|
|
/// This function returns the mate of the given node in the found
|
|
/// matching or \c INVALID if the node is not covered by the matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Node mate(const Node& node) const {
|
|
return (*_matching)[node] != INVALID ?
|
|
_graph.target((*_matching)[node]) : INVALID;
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Dual Solution
|
|
/// Functions to get the dual solution.\n
|
|
/// Either \ref run() or \ref start() function should be called before
|
|
/// using them.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the value of the dual solution.
|
|
///
|
|
/// This function returns the value of the dual solution.
|
|
/// It should be equal to the primal value scaled by \ref dualScale
|
|
/// "dual scale".
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value dualValue() const {
|
|
Value sum = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
sum += nodeValue(n);
|
|
}
|
|
for (int i = 0; i < blossomNum(); ++i) {
|
|
sum += blossomValue(i) * (blossomSize(i) / 2);
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
/// \brief Return the dual value (potential) of the given node.
|
|
///
|
|
/// This function returns the dual value (potential) of the given node.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value nodeValue(const Node& n) const {
|
|
return (*_node_potential)[n];
|
|
}
|
|
|
|
/// \brief Return the number of the blossoms in the basis.
|
|
///
|
|
/// This function returns the number of the blossoms in the basis.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
/// \see BlossomIt
|
|
int blossomNum() const {
|
|
return _blossom_potential.size();
|
|
}
|
|
|
|
/// \brief Return the number of the nodes in the given blossom.
|
|
///
|
|
/// This function returns the number of the nodes in the given blossom.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
/// \see BlossomIt
|
|
int blossomSize(int k) const {
|
|
return _blossom_potential[k].end - _blossom_potential[k].begin;
|
|
}
|
|
|
|
/// \brief Return the dual value (ptential) of the given blossom.
|
|
///
|
|
/// This function returns the dual value (ptential) of the given blossom.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value blossomValue(int k) const {
|
|
return _blossom_potential[k].value;
|
|
}
|
|
|
|
/// \brief Iterator for obtaining the nodes of a blossom.
|
|
///
|
|
/// This class provides an iterator for obtaining the nodes of the
|
|
/// given blossom. It lists a subset of the nodes.
|
|
/// Before using this iterator, you must allocate a
|
|
/// MaxWeightedMatching class and execute it.
|
|
class BlossomIt {
|
|
public:
|
|
|
|
/// \brief Constructor.
|
|
///
|
|
/// Constructor to get the nodes of the given variable.
|
|
///
|
|
/// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or
|
|
/// \ref MaxWeightedMatching::start() "algorithm.start()" must be
|
|
/// called before initializing this iterator.
|
|
BlossomIt(const MaxWeightedMatching& algorithm, int variable)
|
|
: _algorithm(&algorithm)
|
|
{
|
|
_index = _algorithm->_blossom_potential[variable].begin;
|
|
_last = _algorithm->_blossom_potential[variable].end;
|
|
}
|
|
|
|
/// \brief Conversion to \c Node.
|
|
///
|
|
/// Conversion to \c Node.
|
|
operator Node() const {
|
|
return _algorithm->_blossom_node_list[_index];
|
|
}
|
|
|
|
/// \brief Increment operator.
|
|
///
|
|
/// Increment operator.
|
|
BlossomIt& operator++() {
|
|
++_index;
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Validity checking
|
|
///
|
|
/// Checks whether the iterator is invalid.
|
|
bool operator==(Invalid) const { return _index == _last; }
|
|
|
|
/// \brief Validity checking
|
|
///
|
|
/// Checks whether the iterator is valid.
|
|
bool operator!=(Invalid) const { return _index != _last; }
|
|
|
|
private:
|
|
const MaxWeightedMatching* _algorithm;
|
|
int _last;
|
|
int _index;
|
|
};
|
|
|
|
/// @}
|
|
|
|
};
|
|
|
|
/// \ingroup matching
|
|
///
|
|
/// \brief Weighted perfect matching in general graphs
|
|
///
|
|
/// This class provides an efficient implementation of Edmond's
|
|
/// maximum weighted perfect matching algorithm. The implementation
|
|
/// is based on extensive use of priority queues and provides
|
|
/// \f$O(nm\log n)\f$ time complexity.
|
|
///
|
|
/// The maximum weighted perfect matching problem is to find a subset of
|
|
/// the edges in an undirected graph with maximum overall weight for which
|
|
/// each node has exactly one incident edge.
|
|
/// It can be formulated with the following linear program.
|
|
/// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
|
|
/** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
|
|
\quad \forall B\in\mathcal{O}\f] */
|
|
/// \f[x_e \ge 0\quad \forall e\in E\f]
|
|
/// \f[\max \sum_{e\in E}x_ew_e\f]
|
|
/// where \f$\delta(X)\f$ is the set of edges incident to a node in
|
|
/// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
|
|
/// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
|
|
/// subsets of the nodes.
|
|
///
|
|
/// The algorithm calculates an optimal matching and a proof of the
|
|
/// optimality. The solution of the dual problem can be used to check
|
|
/// the result of the algorithm. The dual linear problem is the
|
|
/// following.
|
|
/** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
|
|
w_{uv} \quad \forall uv\in E\f] */
|
|
/// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
|
|
/** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
|
|
\frac{\vert B \vert - 1}{2}z_B\f] */
|
|
///
|
|
/// The algorithm can be executed with the run() function.
|
|
/// After it the matching (the primal solution) and the dual solution
|
|
/// can be obtained using the query functions and the
|
|
/// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class,
|
|
/// which is able to iterate on the nodes of a blossom.
|
|
/// If the value type is integer, then the dual solution is multiplied
|
|
/// by \ref MaxWeightedMatching::dualScale "4".
|
|
///
|
|
/// \tparam GR The undirected graph type the algorithm runs on.
|
|
/// \tparam WM The type edge weight map. The default type is
|
|
/// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
|
|
#ifdef DOXYGEN
|
|
template <typename GR, typename WM>
|
|
#else
|
|
template <typename GR,
|
|
typename WM = typename GR::template EdgeMap<int> >
|
|
#endif
|
|
class MaxWeightedPerfectMatching {
|
|
public:
|
|
|
|
/// The graph type of the algorithm
|
|
typedef GR Graph;
|
|
/// The type of the edge weight map
|
|
typedef WM WeightMap;
|
|
/// The value type of the edge weights
|
|
typedef typename WeightMap::Value Value;
|
|
|
|
/// \brief Scaling factor for dual solution
|
|
///
|
|
/// Scaling factor for dual solution, it is equal to 4 or 1
|
|
/// according to the value type.
|
|
static const int dualScale =
|
|
std::numeric_limits<Value>::is_integer ? 4 : 1;
|
|
|
|
/// The type of the matching map
|
|
typedef typename Graph::template NodeMap<typename Graph::Arc>
|
|
MatchingMap;
|
|
|
|
private:
|
|
|
|
TEMPLATE_GRAPH_TYPEDEFS(Graph);
|
|
|
|
typedef typename Graph::template NodeMap<Value> NodePotential;
|
|
typedef std::vector<Node> BlossomNodeList;
|
|
|
|
struct BlossomVariable {
|
|
int begin, end;
|
|
Value value;
|
|
|
|
BlossomVariable(int _begin, int _end, Value _value)
|
|
: begin(_begin), end(_end), value(_value) {}
|
|
|
|
};
|
|
|
|
typedef std::vector<BlossomVariable> BlossomPotential;
|
|
|
|
const Graph& _graph;
|
|
const WeightMap& _weight;
|
|
|
|
MatchingMap* _matching;
|
|
|
|
NodePotential* _node_potential;
|
|
|
|
BlossomPotential _blossom_potential;
|
|
BlossomNodeList _blossom_node_list;
|
|
|
|
int _node_num;
|
|
int _blossom_num;
|
|
|
|
typedef RangeMap<int> IntIntMap;
|
|
|
|
enum Status {
|
|
EVEN = -1, MATCHED = 0, ODD = 1
|
|
};
|
|
|
|
typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
|
|
struct BlossomData {
|
|
int tree;
|
|
Status status;
|
|
Arc pred, next;
|
|
Value pot, offset;
|
|
};
|
|
|
|
IntNodeMap *_blossom_index;
|
|
BlossomSet *_blossom_set;
|
|
RangeMap<BlossomData>* _blossom_data;
|
|
|
|
IntNodeMap *_node_index;
|
|
IntArcMap *_node_heap_index;
|
|
|
|
struct NodeData {
|
|
|
|
NodeData(IntArcMap& node_heap_index)
|
|
: heap(node_heap_index) {}
|
|
|
|
int blossom;
|
|
Value pot;
|
|
BinHeap<Value, IntArcMap> heap;
|
|
std::map<int, Arc> heap_index;
|
|
|
|
int tree;
|
|
};
|
|
|
|
RangeMap<NodeData>* _node_data;
|
|
|
|
typedef ExtendFindEnum<IntIntMap> TreeSet;
|
|
|
|
IntIntMap *_tree_set_index;
|
|
TreeSet *_tree_set;
|
|
|
|
IntIntMap *_delta2_index;
|
|
BinHeap<Value, IntIntMap> *_delta2;
|
|
|
|
IntEdgeMap *_delta3_index;
|
|
BinHeap<Value, IntEdgeMap> *_delta3;
|
|
|
|
IntIntMap *_delta4_index;
|
|
BinHeap<Value, IntIntMap> *_delta4;
|
|
|
|
Value _delta_sum;
|
|
int _unmatched;
|
|
|
|
typedef MaxWeightedPerfectFractionalMatching<Graph, WeightMap>
|
|
FractionalMatching;
|
|
FractionalMatching *_fractional;
|
|
|
|
void createStructures() {
|
|
_node_num = countNodes(_graph);
|
|
_blossom_num = _node_num * 3 / 2;
|
|
|
|
if (!_matching) {
|
|
_matching = new MatchingMap(_graph);
|
|
}
|
|
|
|
if (!_node_potential) {
|
|
_node_potential = new NodePotential(_graph);
|
|
}
|
|
|
|
if (!_blossom_set) {
|
|
_blossom_index = new IntNodeMap(_graph);
|
|
_blossom_set = new BlossomSet(*_blossom_index);
|
|
_blossom_data = new RangeMap<BlossomData>(_blossom_num);
|
|
} else if (_blossom_data->size() != _blossom_num) {
|
|
delete _blossom_data;
|
|
_blossom_data = new RangeMap<BlossomData>(_blossom_num);
|
|
}
|
|
|
|
if (!_node_index) {
|
|
_node_index = new IntNodeMap(_graph);
|
|
_node_heap_index = new IntArcMap(_graph);
|
|
_node_data = new RangeMap<NodeData>(_node_num,
|
|
NodeData(*_node_heap_index));
|
|
} else if (_node_data->size() != _node_num) {
|
|
delete _node_data;
|
|
_node_data = new RangeMap<NodeData>(_node_num,
|
|
NodeData(*_node_heap_index));
|
|
}
|
|
|
|
if (!_tree_set) {
|
|
_tree_set_index = new IntIntMap(_blossom_num);
|
|
_tree_set = new TreeSet(*_tree_set_index);
|
|
} else {
|
|
_tree_set_index->resize(_blossom_num);
|
|
}
|
|
|
|
if (!_delta2) {
|
|
_delta2_index = new IntIntMap(_blossom_num);
|
|
_delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
|
|
} else {
|
|
_delta2_index->resize(_blossom_num);
|
|
}
|
|
|
|
if (!_delta3) {
|
|
_delta3_index = new IntEdgeMap(_graph);
|
|
_delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
|
|
}
|
|
|
|
if (!_delta4) {
|
|
_delta4_index = new IntIntMap(_blossom_num);
|
|
_delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
|
|
} else {
|
|
_delta4_index->resize(_blossom_num);
|
|
}
|
|
}
|
|
|
|
void destroyStructures() {
|
|
if (_matching) {
|
|
delete _matching;
|
|
}
|
|
if (_node_potential) {
|
|
delete _node_potential;
|
|
}
|
|
if (_blossom_set) {
|
|
delete _blossom_index;
|
|
delete _blossom_set;
|
|
delete _blossom_data;
|
|
}
|
|
|
|
if (_node_index) {
|
|
delete _node_index;
|
|
delete _node_heap_index;
|
|
delete _node_data;
|
|
}
|
|
|
|
if (_tree_set) {
|
|
delete _tree_set_index;
|
|
delete _tree_set;
|
|
}
|
|
if (_delta2) {
|
|
delete _delta2_index;
|
|
delete _delta2;
|
|
}
|
|
if (_delta3) {
|
|
delete _delta3_index;
|
|
delete _delta3;
|
|
}
|
|
if (_delta4) {
|
|
delete _delta4_index;
|
|
delete _delta4;
|
|
}
|
|
}
|
|
|
|
void matchedToEven(int blossom, int tree) {
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
(*_blossom_data)[blossom].pot -=
|
|
2 * (_delta_sum - (*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
|
|
_blossom_set->increase(n, std::numeric_limits<Value>::max());
|
|
int ni = (*_node_index)[n];
|
|
|
|
(*_node_data)[ni].heap.clear();
|
|
(*_node_data)[ni].heap_index.clear();
|
|
|
|
(*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
|
|
_delta3->push(e, rw / 2);
|
|
}
|
|
} else {
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
if ((*_node_data)[vi].heap[it->second] > rw) {
|
|
(*_node_data)[vi].heap.replace(it->second, e);
|
|
(*_node_data)[vi].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[vi].heap.push(e, rw);
|
|
(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
|
|
}
|
|
|
|
if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_delta2->state(vb) != _delta2->IN_HEAP) {
|
|
_delta2->push(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset){
|
|
_delta2->decrease(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
}
|
|
|
|
void matchedToOdd(int blossom) {
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
(*_blossom_data)[blossom].offset += _delta_sum;
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
}
|
|
|
|
void evenToMatched(int blossom, int tree) {
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
(*_blossom_data)[blossom].pot += 2 * _delta_sum;
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
int ni = (*_node_index)[n];
|
|
(*_node_data)[ni].pot -= _delta_sum;
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if (vb == blossom) {
|
|
if (_delta3->state(e) == _delta3->IN_HEAP) {
|
|
_delta3->erase(e);
|
|
}
|
|
} else if ((*_blossom_data)[vb].status == EVEN) {
|
|
|
|
if (_delta3->state(e) == _delta3->IN_HEAP) {
|
|
_delta3->erase(e);
|
|
}
|
|
|
|
int vt = _tree_set->find(vb);
|
|
|
|
if (vt != tree) {
|
|
|
|
Arc r = _graph.oppositeArc(e);
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[ni].heap_index.find(vt);
|
|
|
|
if (it != (*_node_data)[ni].heap_index.end()) {
|
|
if ((*_node_data)[ni].heap[it->second] > rw) {
|
|
(*_node_data)[ni].heap.replace(it->second, r);
|
|
(*_node_data)[ni].heap.decrease(r, rw);
|
|
it->second = r;
|
|
}
|
|
} else {
|
|
(*_node_data)[ni].heap.push(r, rw);
|
|
(*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
|
|
}
|
|
|
|
if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
|
|
_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
|
|
|
|
if (_delta2->state(blossom) != _delta2->IN_HEAP) {
|
|
_delta2->push(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
} else if ((*_delta2)[blossom] >
|
|
_blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset){
|
|
_delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
(*_node_data)[vi].heap.erase(it->second);
|
|
(*_node_data)[vi].heap_index.erase(it);
|
|
if ((*_node_data)[vi].heap.empty()) {
|
|
_blossom_set->increase(v, std::numeric_limits<Value>::max());
|
|
} else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->increase(v, (*_node_data)[vi].heap.prio());
|
|
}
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_blossom_set->classPrio(vb) ==
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->erase(vb);
|
|
} else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset) {
|
|
_delta2->increase(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void oddToMatched(int blossom) {
|
|
(*_blossom_data)[blossom].offset -= _delta_sum;
|
|
|
|
if (_blossom_set->classPrio(blossom) !=
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->push(blossom, _blossom_set->classPrio(blossom) -
|
|
(*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->erase(blossom);
|
|
}
|
|
}
|
|
|
|
void oddToEven(int blossom, int tree) {
|
|
if (!_blossom_set->trivial(blossom)) {
|
|
_delta4->erase(blossom);
|
|
(*_blossom_data)[blossom].pot -=
|
|
2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
|
|
}
|
|
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
|
|
n != INVALID; ++n) {
|
|
int ni = (*_node_index)[n];
|
|
|
|
_blossom_set->increase(n, std::numeric_limits<Value>::max());
|
|
|
|
(*_node_data)[ni].heap.clear();
|
|
(*_node_data)[ni].heap_index.clear();
|
|
(*_node_data)[ni].pot +=
|
|
2 * _delta_sum - (*_blossom_data)[blossom].offset;
|
|
|
|
for (InArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.source(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
|
|
_delta3->push(e, rw / 2);
|
|
}
|
|
} else {
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[vi].heap_index.find(tree);
|
|
|
|
if (it != (*_node_data)[vi].heap_index.end()) {
|
|
if ((*_node_data)[vi].heap[it->second] > rw) {
|
|
(*_node_data)[vi].heap.replace(it->second, e);
|
|
(*_node_data)[vi].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[vi].heap.push(e, rw);
|
|
(*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
|
|
}
|
|
|
|
if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
|
|
_blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
|
|
|
|
if ((*_blossom_data)[vb].status == MATCHED) {
|
|
if (_delta2->state(vb) != _delta2->IN_HEAP) {
|
|
_delta2->push(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
} else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset) {
|
|
_delta2->decrease(vb, _blossom_set->classPrio(vb) -
|
|
(*_blossom_data)[vb].offset);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
}
|
|
|
|
void alternatePath(int even, int tree) {
|
|
int odd;
|
|
|
|
evenToMatched(even, tree);
|
|
(*_blossom_data)[even].status = MATCHED;
|
|
|
|
while ((*_blossom_data)[even].pred != INVALID) {
|
|
odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
|
|
(*_blossom_data)[odd].status = MATCHED;
|
|
oddToMatched(odd);
|
|
(*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
|
|
|
|
even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
|
|
(*_blossom_data)[even].status = MATCHED;
|
|
evenToMatched(even, tree);
|
|
(*_blossom_data)[even].next =
|
|
_graph.oppositeArc((*_blossom_data)[odd].pred);
|
|
}
|
|
|
|
}
|
|
|
|
void destroyTree(int tree) {
|
|
for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
|
|
if ((*_blossom_data)[b].status == EVEN) {
|
|
(*_blossom_data)[b].status = MATCHED;
|
|
evenToMatched(b, tree);
|
|
} else if ((*_blossom_data)[b].status == ODD) {
|
|
(*_blossom_data)[b].status = MATCHED;
|
|
oddToMatched(b);
|
|
}
|
|
}
|
|
_tree_set->eraseClass(tree);
|
|
}
|
|
|
|
void augmentOnEdge(const Edge& edge) {
|
|
|
|
int left = _blossom_set->find(_graph.u(edge));
|
|
int right = _blossom_set->find(_graph.v(edge));
|
|
|
|
int left_tree = _tree_set->find(left);
|
|
alternatePath(left, left_tree);
|
|
destroyTree(left_tree);
|
|
|
|
int right_tree = _tree_set->find(right);
|
|
alternatePath(right, right_tree);
|
|
destroyTree(right_tree);
|
|
|
|
(*_blossom_data)[left].next = _graph.direct(edge, true);
|
|
(*_blossom_data)[right].next = _graph.direct(edge, false);
|
|
}
|
|
|
|
void extendOnArc(const Arc& arc) {
|
|
int base = _blossom_set->find(_graph.target(arc));
|
|
int tree = _tree_set->find(base);
|
|
|
|
int odd = _blossom_set->find(_graph.source(arc));
|
|
_tree_set->insert(odd, tree);
|
|
(*_blossom_data)[odd].status = ODD;
|
|
matchedToOdd(odd);
|
|
(*_blossom_data)[odd].pred = arc;
|
|
|
|
int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
|
|
(*_blossom_data)[even].pred = (*_blossom_data)[even].next;
|
|
_tree_set->insert(even, tree);
|
|
(*_blossom_data)[even].status = EVEN;
|
|
matchedToEven(even, tree);
|
|
}
|
|
|
|
void shrinkOnEdge(const Edge& edge, int tree) {
|
|
int nca = -1;
|
|
std::vector<int> left_path, right_path;
|
|
|
|
{
|
|
std::set<int> left_set, right_set;
|
|
int left = _blossom_set->find(_graph.u(edge));
|
|
left_path.push_back(left);
|
|
left_set.insert(left);
|
|
|
|
int right = _blossom_set->find(_graph.v(edge));
|
|
right_path.push_back(right);
|
|
right_set.insert(right);
|
|
|
|
while (true) {
|
|
|
|
if ((*_blossom_data)[left].pred == INVALID) break;
|
|
|
|
left =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
|
|
left_path.push_back(left);
|
|
left =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[left].pred));
|
|
left_path.push_back(left);
|
|
|
|
left_set.insert(left);
|
|
|
|
if (right_set.find(left) != right_set.end()) {
|
|
nca = left;
|
|
break;
|
|
}
|
|
|
|
if ((*_blossom_data)[right].pred == INVALID) break;
|
|
|
|
right =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
|
|
right_path.push_back(right);
|
|
right =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[right].pred));
|
|
right_path.push_back(right);
|
|
|
|
right_set.insert(right);
|
|
|
|
if (left_set.find(right) != left_set.end()) {
|
|
nca = right;
|
|
break;
|
|
}
|
|
|
|
}
|
|
|
|
if (nca == -1) {
|
|
if ((*_blossom_data)[left].pred == INVALID) {
|
|
nca = right;
|
|
while (left_set.find(nca) == left_set.end()) {
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
right_path.push_back(nca);
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
right_path.push_back(nca);
|
|
}
|
|
} else {
|
|
nca = left;
|
|
while (right_set.find(nca) == right_set.end()) {
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
left_path.push_back(nca);
|
|
nca =
|
|
_blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
|
|
left_path.push_back(nca);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
std::vector<int> subblossoms;
|
|
Arc prev;
|
|
|
|
prev = _graph.direct(edge, true);
|
|
for (int i = 0; left_path[i] != nca; i += 2) {
|
|
subblossoms.push_back(left_path[i]);
|
|
(*_blossom_data)[left_path[i]].next = prev;
|
|
_tree_set->erase(left_path[i]);
|
|
|
|
subblossoms.push_back(left_path[i + 1]);
|
|
(*_blossom_data)[left_path[i + 1]].status = EVEN;
|
|
oddToEven(left_path[i + 1], tree);
|
|
_tree_set->erase(left_path[i + 1]);
|
|
prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
|
|
}
|
|
|
|
int k = 0;
|
|
while (right_path[k] != nca) ++k;
|
|
|
|
subblossoms.push_back(nca);
|
|
(*_blossom_data)[nca].next = prev;
|
|
|
|
for (int i = k - 2; i >= 0; i -= 2) {
|
|
subblossoms.push_back(right_path[i + 1]);
|
|
(*_blossom_data)[right_path[i + 1]].status = EVEN;
|
|
oddToEven(right_path[i + 1], tree);
|
|
_tree_set->erase(right_path[i + 1]);
|
|
|
|
(*_blossom_data)[right_path[i + 1]].next =
|
|
(*_blossom_data)[right_path[i + 1]].pred;
|
|
|
|
subblossoms.push_back(right_path[i]);
|
|
_tree_set->erase(right_path[i]);
|
|
}
|
|
|
|
int surface =
|
|
_blossom_set->join(subblossoms.begin(), subblossoms.end());
|
|
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (!_blossom_set->trivial(subblossoms[i])) {
|
|
(*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
|
|
}
|
|
(*_blossom_data)[subblossoms[i]].status = MATCHED;
|
|
}
|
|
|
|
(*_blossom_data)[surface].pot = -2 * _delta_sum;
|
|
(*_blossom_data)[surface].offset = 0;
|
|
(*_blossom_data)[surface].status = EVEN;
|
|
(*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
|
|
(*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
|
|
|
|
_tree_set->insert(surface, tree);
|
|
_tree_set->erase(nca);
|
|
}
|
|
|
|
void splitBlossom(int blossom) {
|
|
Arc next = (*_blossom_data)[blossom].next;
|
|
Arc pred = (*_blossom_data)[blossom].pred;
|
|
|
|
int tree = _tree_set->find(blossom);
|
|
|
|
(*_blossom_data)[blossom].status = MATCHED;
|
|
oddToMatched(blossom);
|
|
if (_delta2->state(blossom) == _delta2->IN_HEAP) {
|
|
_delta2->erase(blossom);
|
|
}
|
|
|
|
std::vector<int> subblossoms;
|
|
_blossom_set->split(blossom, std::back_inserter(subblossoms));
|
|
|
|
Value offset = (*_blossom_data)[blossom].offset;
|
|
int b = _blossom_set->find(_graph.source(pred));
|
|
int d = _blossom_set->find(_graph.source(next));
|
|
|
|
int ib = -1, id = -1;
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (subblossoms[i] == b) ib = i;
|
|
if (subblossoms[i] == d) id = i;
|
|
|
|
(*_blossom_data)[subblossoms[i]].offset = offset;
|
|
if (!_blossom_set->trivial(subblossoms[i])) {
|
|
(*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
|
|
}
|
|
if (_blossom_set->classPrio(subblossoms[i]) !=
|
|
std::numeric_limits<Value>::max()) {
|
|
_delta2->push(subblossoms[i],
|
|
_blossom_set->classPrio(subblossoms[i]) -
|
|
(*_blossom_data)[subblossoms[i]].offset);
|
|
}
|
|
}
|
|
|
|
if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
|
|
for (int i = (id + 1) % subblossoms.size();
|
|
i != ib; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
}
|
|
|
|
for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
int ub = subblossoms[(i + 2) % subblossoms.size()];
|
|
|
|
(*_blossom_data)[sb].status = ODD;
|
|
matchedToOdd(sb);
|
|
_tree_set->insert(sb, tree);
|
|
(*_blossom_data)[sb].pred = pred;
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
|
|
pred = (*_blossom_data)[ub].next;
|
|
|
|
(*_blossom_data)[tb].status = EVEN;
|
|
matchedToEven(tb, tree);
|
|
_tree_set->insert(tb, tree);
|
|
(*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
|
|
}
|
|
|
|
(*_blossom_data)[subblossoms[id]].status = ODD;
|
|
matchedToOdd(subblossoms[id]);
|
|
_tree_set->insert(subblossoms[id], tree);
|
|
(*_blossom_data)[subblossoms[id]].next = next;
|
|
(*_blossom_data)[subblossoms[id]].pred = pred;
|
|
|
|
} else {
|
|
|
|
for (int i = (ib + 1) % subblossoms.size();
|
|
i != id; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
(*_blossom_data)[sb].next =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
}
|
|
|
|
for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
|
|
int sb = subblossoms[i];
|
|
int tb = subblossoms[(i + 1) % subblossoms.size()];
|
|
int ub = subblossoms[(i + 2) % subblossoms.size()];
|
|
|
|
(*_blossom_data)[sb].status = ODD;
|
|
matchedToOdd(sb);
|
|
_tree_set->insert(sb, tree);
|
|
(*_blossom_data)[sb].next = next;
|
|
(*_blossom_data)[sb].pred =
|
|
_graph.oppositeArc((*_blossom_data)[tb].next);
|
|
|
|
(*_blossom_data)[tb].status = EVEN;
|
|
matchedToEven(tb, tree);
|
|
_tree_set->insert(tb, tree);
|
|
(*_blossom_data)[tb].pred =
|
|
(*_blossom_data)[tb].next =
|
|
_graph.oppositeArc((*_blossom_data)[ub].next);
|
|
next = (*_blossom_data)[ub].next;
|
|
}
|
|
|
|
(*_blossom_data)[subblossoms[ib]].status = ODD;
|
|
matchedToOdd(subblossoms[ib]);
|
|
_tree_set->insert(subblossoms[ib], tree);
|
|
(*_blossom_data)[subblossoms[ib]].next = next;
|
|
(*_blossom_data)[subblossoms[ib]].pred = pred;
|
|
}
|
|
_tree_set->erase(blossom);
|
|
}
|
|
|
|
void extractBlossom(int blossom, const Node& base, const Arc& matching) {
|
|
if (_blossom_set->trivial(blossom)) {
|
|
int bi = (*_node_index)[base];
|
|
Value pot = (*_node_data)[bi].pot;
|
|
|
|
(*_matching)[base] = matching;
|
|
_blossom_node_list.push_back(base);
|
|
(*_node_potential)[base] = pot;
|
|
} else {
|
|
|
|
Value pot = (*_blossom_data)[blossom].pot;
|
|
int bn = _blossom_node_list.size();
|
|
|
|
std::vector<int> subblossoms;
|
|
_blossom_set->split(blossom, std::back_inserter(subblossoms));
|
|
int b = _blossom_set->find(base);
|
|
int ib = -1;
|
|
for (int i = 0; i < int(subblossoms.size()); ++i) {
|
|
if (subblossoms[i] == b) { ib = i; break; }
|
|
}
|
|
|
|
for (int i = 1; i < int(subblossoms.size()); i += 2) {
|
|
int sb = subblossoms[(ib + i) % subblossoms.size()];
|
|
int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
|
|
|
|
Arc m = (*_blossom_data)[tb].next;
|
|
extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
|
|
extractBlossom(tb, _graph.source(m), m);
|
|
}
|
|
extractBlossom(subblossoms[ib], base, matching);
|
|
|
|
int en = _blossom_node_list.size();
|
|
|
|
_blossom_potential.push_back(BlossomVariable(bn, en, pot));
|
|
}
|
|
}
|
|
|
|
void extractMatching() {
|
|
std::vector<int> blossoms;
|
|
for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
|
|
blossoms.push_back(c);
|
|
}
|
|
|
|
for (int i = 0; i < int(blossoms.size()); ++i) {
|
|
|
|
Value offset = (*_blossom_data)[blossoms[i]].offset;
|
|
(*_blossom_data)[blossoms[i]].pot += 2 * offset;
|
|
for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
|
|
n != INVALID; ++n) {
|
|
(*_node_data)[(*_node_index)[n]].pot -= offset;
|
|
}
|
|
|
|
Arc matching = (*_blossom_data)[blossoms[i]].next;
|
|
Node base = _graph.source(matching);
|
|
extractBlossom(blossoms[i], base, matching);
|
|
}
|
|
}
|
|
|
|
public:
|
|
|
|
/// \brief Constructor
|
|
///
|
|
/// Constructor.
|
|
MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
|
|
: _graph(graph), _weight(weight), _matching(0),
|
|
_node_potential(0), _blossom_potential(), _blossom_node_list(),
|
|
_node_num(0), _blossom_num(0),
|
|
|
|
_blossom_index(0), _blossom_set(0), _blossom_data(0),
|
|
_node_index(0), _node_heap_index(0), _node_data(0),
|
|
_tree_set_index(0), _tree_set(0),
|
|
|
|
_delta2_index(0), _delta2(0),
|
|
_delta3_index(0), _delta3(0),
|
|
_delta4_index(0), _delta4(0),
|
|
|
|
_delta_sum(), _unmatched(0),
|
|
|
|
_fractional(0)
|
|
{}
|
|
|
|
~MaxWeightedPerfectMatching() {
|
|
destroyStructures();
|
|
if (_fractional) {
|
|
delete _fractional;
|
|
}
|
|
}
|
|
|
|
/// \name Execution Control
|
|
/// The simplest way to execute the algorithm is to use the
|
|
/// \ref run() member function.
|
|
|
|
///@{
|
|
|
|
/// \brief Initialize the algorithm
|
|
///
|
|
/// This function initializes the algorithm.
|
|
void init() {
|
|
createStructures();
|
|
|
|
_blossom_node_list.clear();
|
|
_blossom_potential.clear();
|
|
|
|
for (ArcIt e(_graph); e != INVALID; ++e) {
|
|
(*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
(*_delta3_index)[e] = _delta3->PRE_HEAP;
|
|
}
|
|
for (int i = 0; i < _blossom_num; ++i) {
|
|
(*_delta2_index)[i] = _delta2->PRE_HEAP;
|
|
(*_delta4_index)[i] = _delta4->PRE_HEAP;
|
|
}
|
|
|
|
_unmatched = _node_num;
|
|
|
|
_delta2->clear();
|
|
_delta3->clear();
|
|
_delta4->clear();
|
|
_blossom_set->clear();
|
|
_tree_set->clear();
|
|
|
|
int index = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
Value max = - std::numeric_limits<Value>::max();
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
if (_graph.target(e) == n) continue;
|
|
if ((dualScale * _weight[e]) / 2 > max) {
|
|
max = (dualScale * _weight[e]) / 2;
|
|
}
|
|
}
|
|
(*_node_index)[n] = index;
|
|
(*_node_data)[index].heap_index.clear();
|
|
(*_node_data)[index].heap.clear();
|
|
(*_node_data)[index].pot = max;
|
|
int blossom =
|
|
_blossom_set->insert(n, std::numeric_limits<Value>::max());
|
|
|
|
_tree_set->insert(blossom);
|
|
|
|
(*_blossom_data)[blossom].status = EVEN;
|
|
(*_blossom_data)[blossom].pred = INVALID;
|
|
(*_blossom_data)[blossom].next = INVALID;
|
|
(*_blossom_data)[blossom].pot = 0;
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
++index;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
int si = (*_node_index)[_graph.u(e)];
|
|
int ti = (*_node_index)[_graph.v(e)];
|
|
if (_graph.u(e) != _graph.v(e)) {
|
|
_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
|
|
dualScale * _weight[e]) / 2);
|
|
}
|
|
}
|
|
}
|
|
|
|
/// \brief Initialize the algorithm with fractional matching
|
|
///
|
|
/// This function initializes the algorithm with a fractional
|
|
/// matching. This initialization is also called jumpstart heuristic.
|
|
void fractionalInit() {
|
|
createStructures();
|
|
|
|
_blossom_node_list.clear();
|
|
_blossom_potential.clear();
|
|
|
|
if (_fractional == 0) {
|
|
_fractional = new FractionalMatching(_graph, _weight, false);
|
|
}
|
|
if (!_fractional->run()) {
|
|
_unmatched = -1;
|
|
return;
|
|
}
|
|
|
|
for (ArcIt e(_graph); e != INVALID; ++e) {
|
|
(*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
|
|
}
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
(*_delta3_index)[e] = _delta3->PRE_HEAP;
|
|
}
|
|
for (int i = 0; i < _blossom_num; ++i) {
|
|
(*_delta2_index)[i] = _delta2->PRE_HEAP;
|
|
(*_delta4_index)[i] = _delta4->PRE_HEAP;
|
|
}
|
|
|
|
_unmatched = 0;
|
|
|
|
_delta2->clear();
|
|
_delta3->clear();
|
|
_delta4->clear();
|
|
_blossom_set->clear();
|
|
_tree_set->clear();
|
|
|
|
int index = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
Value pot = _fractional->nodeValue(n);
|
|
(*_node_index)[n] = index;
|
|
(*_node_data)[index].pot = pot;
|
|
(*_node_data)[index].heap_index.clear();
|
|
(*_node_data)[index].heap.clear();
|
|
int blossom =
|
|
_blossom_set->insert(n, std::numeric_limits<Value>::max());
|
|
|
|
(*_blossom_data)[blossom].status = MATCHED;
|
|
(*_blossom_data)[blossom].pred = INVALID;
|
|
(*_blossom_data)[blossom].next = _fractional->matching(n);
|
|
(*_blossom_data)[blossom].pot = 0;
|
|
(*_blossom_data)[blossom].offset = 0;
|
|
++index;
|
|
}
|
|
|
|
typename Graph::template NodeMap<bool> processed(_graph, false);
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if (processed[n]) continue;
|
|
processed[n] = true;
|
|
if (_fractional->matching(n) == INVALID) continue;
|
|
int num = 1;
|
|
Node v = _graph.target(_fractional->matching(n));
|
|
while (n != v) {
|
|
processed[v] = true;
|
|
v = _graph.target(_fractional->matching(v));
|
|
++num;
|
|
}
|
|
|
|
if (num % 2 == 1) {
|
|
std::vector<int> subblossoms(num);
|
|
|
|
subblossoms[--num] = _blossom_set->find(n);
|
|
v = _graph.target(_fractional->matching(n));
|
|
while (n != v) {
|
|
subblossoms[--num] = _blossom_set->find(v);
|
|
v = _graph.target(_fractional->matching(v));
|
|
}
|
|
|
|
int surface =
|
|
_blossom_set->join(subblossoms.begin(), subblossoms.end());
|
|
(*_blossom_data)[surface].status = EVEN;
|
|
(*_blossom_data)[surface].pred = INVALID;
|
|
(*_blossom_data)[surface].next = INVALID;
|
|
(*_blossom_data)[surface].pot = 0;
|
|
(*_blossom_data)[surface].offset = 0;
|
|
|
|
_tree_set->insert(surface);
|
|
++_unmatched;
|
|
}
|
|
}
|
|
|
|
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
|
int si = (*_node_index)[_graph.u(e)];
|
|
int sb = _blossom_set->find(_graph.u(e));
|
|
int ti = (*_node_index)[_graph.v(e)];
|
|
int tb = _blossom_set->find(_graph.v(e));
|
|
if ((*_blossom_data)[sb].status == EVEN &&
|
|
(*_blossom_data)[tb].status == EVEN && sb != tb) {
|
|
_delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
|
|
dualScale * _weight[e]) / 2);
|
|
}
|
|
}
|
|
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
int nb = _blossom_set->find(n);
|
|
if ((*_blossom_data)[nb].status != MATCHED) continue;
|
|
int ni = (*_node_index)[n];
|
|
|
|
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
Node v = _graph.target(e);
|
|
int vb = _blossom_set->find(v);
|
|
int vi = (*_node_index)[v];
|
|
|
|
Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
|
|
dualScale * _weight[e];
|
|
|
|
if ((*_blossom_data)[vb].status == EVEN) {
|
|
|
|
int vt = _tree_set->find(vb);
|
|
|
|
typename std::map<int, Arc>::iterator it =
|
|
(*_node_data)[ni].heap_index.find(vt);
|
|
|
|
if (it != (*_node_data)[ni].heap_index.end()) {
|
|
if ((*_node_data)[ni].heap[it->second] > rw) {
|
|
(*_node_data)[ni].heap.replace(it->second, e);
|
|
(*_node_data)[ni].heap.decrease(e, rw);
|
|
it->second = e;
|
|
}
|
|
} else {
|
|
(*_node_data)[ni].heap.push(e, rw);
|
|
(*_node_data)[ni].heap_index.insert(std::make_pair(vt, e));
|
|
}
|
|
}
|
|
}
|
|
|
|
if (!(*_node_data)[ni].heap.empty()) {
|
|
_blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
|
|
_delta2->push(nb, _blossom_set->classPrio(nb));
|
|
}
|
|
}
|
|
}
|
|
|
|
/// \brief Start the algorithm
|
|
///
|
|
/// This function starts the algorithm.
|
|
///
|
|
/// \pre \ref init() or \ref fractionalInit() must be called before
|
|
/// using this function.
|
|
bool start() {
|
|
enum OpType {
|
|
D2, D3, D4
|
|
};
|
|
|
|
if (_unmatched == -1) return false;
|
|
|
|
while (_unmatched > 0) {
|
|
Value d2 = !_delta2->empty() ?
|
|
_delta2->prio() : std::numeric_limits<Value>::max();
|
|
|
|
Value d3 = !_delta3->empty() ?
|
|
_delta3->prio() : std::numeric_limits<Value>::max();
|
|
|
|
Value d4 = !_delta4->empty() ?
|
|
_delta4->prio() : std::numeric_limits<Value>::max();
|
|
|
|
_delta_sum = d3; OpType ot = D3;
|
|
if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
|
|
if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
|
|
|
|
if (_delta_sum == std::numeric_limits<Value>::max()) {
|
|
return false;
|
|
}
|
|
|
|
switch (ot) {
|
|
case D2:
|
|
{
|
|
int blossom = _delta2->top();
|
|
Node n = _blossom_set->classTop(blossom);
|
|
Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
|
|
extendOnArc(e);
|
|
}
|
|
break;
|
|
case D3:
|
|
{
|
|
Edge e = _delta3->top();
|
|
|
|
int left_blossom = _blossom_set->find(_graph.u(e));
|
|
int right_blossom = _blossom_set->find(_graph.v(e));
|
|
|
|
if (left_blossom == right_blossom) {
|
|
_delta3->pop();
|
|
} else {
|
|
int left_tree = _tree_set->find(left_blossom);
|
|
int right_tree = _tree_set->find(right_blossom);
|
|
|
|
if (left_tree == right_tree) {
|
|
shrinkOnEdge(e, left_tree);
|
|
} else {
|
|
augmentOnEdge(e);
|
|
_unmatched -= 2;
|
|
}
|
|
}
|
|
} break;
|
|
case D4:
|
|
splitBlossom(_delta4->top());
|
|
break;
|
|
}
|
|
}
|
|
extractMatching();
|
|
return true;
|
|
}
|
|
|
|
/// \brief Run the algorithm.
|
|
///
|
|
/// This method runs the \c %MaxWeightedPerfectMatching algorithm.
|
|
///
|
|
/// \note mwpm.run() is just a shortcut of the following code.
|
|
/// \code
|
|
/// mwpm.fractionalInit();
|
|
/// mwpm.start();
|
|
/// \endcode
|
|
bool run() {
|
|
fractionalInit();
|
|
return start();
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Primal Solution
|
|
/// Functions to get the primal solution, i.e. the maximum weighted
|
|
/// perfect matching.\n
|
|
/// Either \ref run() or \ref start() function should be called before
|
|
/// using them.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the weight of the matching.
|
|
///
|
|
/// This function returns the weight of the found matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value matchingWeight() const {
|
|
Value sum = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
if ((*_matching)[n] != INVALID) {
|
|
sum += _weight[(*_matching)[n]];
|
|
}
|
|
}
|
|
return sum / 2;
|
|
}
|
|
|
|
/// \brief Return \c true if the given edge is in the matching.
|
|
///
|
|
/// This function returns \c true if the given edge is in the found
|
|
/// matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
bool matching(const Edge& edge) const {
|
|
return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
|
|
}
|
|
|
|
/// \brief Return the matching arc (or edge) incident to the given node.
|
|
///
|
|
/// This function returns the matching arc (or edge) incident to the
|
|
/// given node in the found matching or \c INVALID if the node is
|
|
/// not covered by the matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Arc matching(const Node& node) const {
|
|
return (*_matching)[node];
|
|
}
|
|
|
|
/// \brief Return a const reference to the matching map.
|
|
///
|
|
/// This function returns a const reference to a node map that stores
|
|
/// the matching arc (or edge) incident to each node.
|
|
const MatchingMap& matchingMap() const {
|
|
return *_matching;
|
|
}
|
|
|
|
/// \brief Return the mate of the given node.
|
|
///
|
|
/// This function returns the mate of the given node in the found
|
|
/// matching or \c INVALID if the node is not covered by the matching.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Node mate(const Node& node) const {
|
|
return _graph.target((*_matching)[node]);
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Dual Solution
|
|
/// Functions to get the dual solution.\n
|
|
/// Either \ref run() or \ref start() function should be called before
|
|
/// using them.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the value of the dual solution.
|
|
///
|
|
/// This function returns the value of the dual solution.
|
|
/// It should be equal to the primal value scaled by \ref dualScale
|
|
/// "dual scale".
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value dualValue() const {
|
|
Value sum = 0;
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
sum += nodeValue(n);
|
|
}
|
|
for (int i = 0; i < blossomNum(); ++i) {
|
|
sum += blossomValue(i) * (blossomSize(i) / 2);
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
/// \brief Return the dual value (potential) of the given node.
|
|
///
|
|
/// This function returns the dual value (potential) of the given node.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
Value nodeValue(const Node& n) const {
|
|
return (*_node_potential)[n];
|
|
}
|
|
|
|
/// \brief Return the number of the blossoms in the basis.
|
|
///
|
|
/// This function returns the number of the blossoms in the basis.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
/// \see BlossomIt
|
|
int blossomNum() const {
|
|
return _blossom_potential.size();
|
|
}
|
|
|
|
/// \brief Return the number of the nodes in the given blossom.
|
|
///
|
|
/// This function returns the number of the nodes in the given blossom.
|
|
///
|
|
/// \pre Either run() or start() must be called before using this function.
|
|
/// \see BlossomIt
|
|
int blossomSize(int k) const {
|
|
return _blossom_potential[k].end - _blossom_potential[k].begin;
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}
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|
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/// \brief Return the dual value (ptential) of the given blossom.
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|
///
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|
/// This function returns the dual value (ptential) of the given blossom.
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|
///
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|
/// \pre Either run() or start() must be called before using this function.
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Value blossomValue(int k) const {
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|
return _blossom_potential[k].value;
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|
}
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|
|
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/// \brief Iterator for obtaining the nodes of a blossom.
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|
///
|
|
/// This class provides an iterator for obtaining the nodes of the
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|
/// given blossom. It lists a subset of the nodes.
|
|
/// Before using this iterator, you must allocate a
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|
/// MaxWeightedPerfectMatching class and execute it.
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|
class BlossomIt {
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|
public:
|
|
|
|
/// \brief Constructor.
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|
///
|
|
/// Constructor to get the nodes of the given variable.
|
|
///
|
|
/// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()"
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|
/// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()"
|
|
/// must be called before initializing this iterator.
|
|
BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
|
|
: _algorithm(&algorithm)
|
|
{
|
|
_index = _algorithm->_blossom_potential[variable].begin;
|
|
_last = _algorithm->_blossom_potential[variable].end;
|
|
}
|
|
|
|
/// \brief Conversion to \c Node.
|
|
///
|
|
/// Conversion to \c Node.
|
|
operator Node() const {
|
|
return _algorithm->_blossom_node_list[_index];
|
|
}
|
|
|
|
/// \brief Increment operator.
|
|
///
|
|
/// Increment operator.
|
|
BlossomIt& operator++() {
|
|
++_index;
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Validity checking
|
|
///
|
|
/// This function checks whether the iterator is invalid.
|
|
bool operator==(Invalid) const { return _index == _last; }
|
|
|
|
/// \brief Validity checking
|
|
///
|
|
/// This function checks whether the iterator is valid.
|
|
bool operator!=(Invalid) const { return _index != _last; }
|
|
|
|
private:
|
|
const MaxWeightedPerfectMatching* _algorithm;
|
|
int _last;
|
|
int _index;
|
|
};
|
|
|
|
/// @}
|
|
|
|
};
|
|
|
|
} //END OF NAMESPACE LEMON
|
|
|
|
#endif //LEMON_MATCHING_H
|