RhodeCode

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_MATCHING_H

#define LEMON_MATCHING_H

#include <vector>

#include <queue>

#include <set>

#include <limits>

#include <lemon/core.h>

#include <lemon/unionfind.h>

#include <lemon/bin_heap.h>

#include <lemon/maps.h>

///\ingroup matching

///\file

///\brief Maximum matching algorithms in general graphs.

namespace lemon {

  /// \ingroup matching

  ///

  /// \brief Maximum cardinality matching in general graphs

  ///

  /// This class implements Edmonds' alternating forest matching algorithm

  /// for finding a maximum cardinality matching in a general undirected graph.

  /// It can be started from an arbitrary initial matching

  /// (the default is the empty one).

  ///

  /// The dual solution of the problem is a map of the nodes to

  /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),

  /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds

  /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph

  /// with factor-critical components, the nodes in \c ODD/A form the

  /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having

  /// a perfect matching. The number of the factor-critical components

  /// minus the number of barrier nodes is a lower bound on the

      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;

    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);

      }

      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));

      }

          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),

    ~MaxWeightedMatching() {

      destroyStructures();

    }

    /// \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();

      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;

      }

      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].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 Start the algorithm

    ///

    /// This function starts the algorithm.

    ///

    void start() {

      enum OpType {

        D1, D2, D3, D4

      };

        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);

          }

          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);

            } 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);

              }

            }

          } 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.start();

    /// \endcode

    void run() {

      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]];

        }

      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;

    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);

      }

      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));

      }

        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),

    ~MaxWeightedPerfectMatching() {

      destroyStructures();

    }

    /// \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();

      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;

      }

      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].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 Start the algorithm

    ///

    /// This function starts the algorithm.

    ///

    bool start() {

      enum OpType {

        D2, D3, D4

      };

        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);

              }

            }

          } 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.start();

    /// \endcode

    bool run() {

      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]];

        }

  }

  for (int i = 0; i < mwpm.blossomNum(); ++i) {

    check(mwpm.blossomValue(i) >= 0, "Invalid blossom value");

    check(mwpm.blossomSize(i) % 2 == 1, "Even blossom size");

    dv += mwpm.blossomValue(i) * ((mwpm.blossomSize(i) - 1) / 2);

  }

  check(pv * mwpm.dualScale == dv * 2, "Wrong duality");

  return;

}

int main() {

  for (int i = 0; i < lgfn; ++i) {

    SmartGraph graph;

    SmartGraph::EdgeMap<int> weight(graph);

    istringstream lgfs(lgf[i]);

    graphReader(graph, lgfs).

      edgeMap("weight", weight).run();

    }

  }

  return 0;

}