LEMON/LEMON-main Changeset - r760:83ce7ce39f21

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Changeset - r760:83ce7ce39f21

« 759:d66ff3

761:579586 »

r760:83ce7ce39f21

Thu, 06 Aug 2009 20:12:43

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Rework and fix the implementation of MinMeanCycle (#179) - Fix the handling of the cycle means. - Many implementation improvements: - More efficient data storage for the strongly connected components. - Better handling of BFS queues. - Merge consecutive BFS searches (perform two BFS searches instead of three). This version is about two times faster on average and an order of magnitude faster if there are a lot of strongly connected components.

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1 file changed with 188 insertions and 167 deletions:

lemon/min_mean_cycle.h

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lemon/min_mean_cycle.h

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 		/* -*- C++ -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library
+		 *
 		 * Copyright (C) 2003-2008
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_MIN_MEAN_CYCLE_H
 		#define LEMON_MIN_MEAN_CYCLE_H
 		/// \ingroup shortest_path
 		///
 		/// \file
 		/// \brief Howard's algorithm for finding a minimum mean cycle.
 		#include <vector>
 		#include <lemon/core.h>
 		#include <lemon/path.h>
 		#include <lemon/tolerance.h>
 		#include <lemon/connectivity.h>
 		namespace lemon {
 		  /// \addtogroup shortest_path
 		  /// @{
 		  /// \brief Implementation of Howard's algorithm for finding a minimum
 		  /// mean cycle.
 		  ///
 		  /// \ref MinMeanCycle implements Howard's algorithm for finding a
 		  /// directed cycle of minimum mean length (cost) in a digraph.
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// \tparam LEN The type of the length map. The default
 		  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  ///
 		  /// \warning \c LEN::Value must be convertible to \c double.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN>
 		#else
 		  template < typename GR,
 		             typename LEN = typename GR::template ArcMap<int> >
 		#endif
 		  class MinMeanCycle
+		  {
 		  public:
 		    /// The type of the digraph the algorithm runs on
 		    typedef GR Digraph;
 		    /// The type of the length map
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename LengthMap::Value Value;
 		    /// The type of the paths
 		    typedef lemon::Path<Digraph> Path;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    // The digraph the algorithm runs on
 		    const Digraph &_gr;
 		    // The length of the arcs
 		    const LengthMap &_length;
 		    // The total length of the found cycle
 		    Value _cycle_length;
 		    // The number of arcs on the found cycle
 		    int _cycle_size;
-		    // The found cycle
+		    // Data for the found cycles
 		    bool _curr_found, _best_found;
 		    Value _curr_length, _best_length;
 		    int _curr_size, _best_size;
 		    Node _curr_node, _best_node;
 		    Path *_cycle_path;
 		    bool _local_path;
 		    bool _local_path;
 		    bool _cycle_found;
-		    Node _cycle_node;
+		    // Internal data used by the algorithm
 		    typename Digraph::template NodeMap<Arc> _policy;
 		    typename Digraph::template NodeMap<bool> _reached;
 		    typename Digraph::template NodeMap<int> _level;
 		    typename Digraph::template NodeMap<double> _dist;
 		    typename Digraph::template NodeMap<bool> _reached;
 		    typename Digraph::template NodeMap<double> _dist;
 		    typename Digraph::template NodeMap<Arc> _policy;
 		    // Data for storing the strongly connected components
 		    int _comp_num;
 		    typename Digraph::template NodeMap<int> _comp;
 		    int _comp_num;
 		    std::vector<Node> _nodes;
 		    std::vector<Arc> _arcs;
 		    std::vector<std::vector<Node> > _comp_nodes;
 		    std::vector<Node>* _nodes;
 		    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
 		    // Queue used for BFS search
 		    std::vector<Node> _queue;
 		    int _qfront, _qback;
 		    Tolerance<double> _tol;
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param length The lengths (costs) of the arcs.
 		    MinMeanCycle( const Digraph &digraph,
 		                  const LengthMap &length ) :
 		      _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
 		      _cycle_path(NULL), _local_path(false), _reached(digraph),
-		      _dist(digraph), _policy(digraph), _comp(digraph)
+		      _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false),
 		      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
 		      _comp(digraph), _in_arcs(digraph)
 		    {}
 		    /// Destructor.
 		    ~MinMeanCycle() {
 		      if (_local_path) delete _cycle_path;
+		    }
 		    /// \brief Set the path structure for storing the found cycle.
 		    ///
 		    /// This function sets an external path structure for storing the
 		    /// found cycle.
 		    ///
 		    /// If you don't call this function before calling \ref run() or
 		    /// \ref findMinMean(), it will allocate a local \ref Path "path"
 		    /// structure. The destuctor deallocates this automatically
 		    /// allocated object, of course.
 		    ///
 		    /// \note The algorithm calls only the \ref lemon::Path::addBack()
 		    /// "addBack()" function of the given path structure.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    ///
 		    /// \sa cycle()
 		    MinMeanCycle& cyclePath(Path &path) {
 		      if (_local_path) {
 		        delete _cycle_path;
 		        _local_path = false;
+		      }
 		      _cycle_path = &path;
 		      return *this;
+		    }
 		    /// \name Execution control
 		    /// The simplest way to execute the algorithm is to call the \ref run()
 		    /// function.\n
 		    /// If you only need the minimum mean length, you may call
 		    /// \ref findMinMean().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// It can be called more than once (e.g. if the underlying digraph
 		    /// and/or the arc lengths have been modified).
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   return mmc.findMinMean() && mmc.findCycle();
 		    /// \endcode
 		    bool run() {
 		      return findMinMean() && findCycle();
+		    }
 		    /// \brief Find the minimum cycle mean.
 		    ///
 		    /// This function finds the minimum mean length of the directed
 		    /// cycles in the digraph.
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    bool findMinMean() {
 		      // Initialize
 		      _tol.epsilon(1e-6);
 		      if (!_cycle_path) {
 		        _local_path = true;
 		        _cycle_path = new Path;
+		      }
 		      _cycle_path->clear();
 		      _cycle_found = false;
+		      // Initialize and find strongly connected components
 		      init();
 		      findComponents();
 		      // Find the minimum cycle mean in the components
 		      _comp_num = stronglyConnectedComponents(_gr, _comp);
 		      for (int comp = 0; comp < _comp_num; ++comp) {
-		        if (!initCurrentComponent(comp)) continue;
+		        // Find the minimum mean cycle in the current component
 		        if (!buildPolicyGraph(comp)) continue;
 		        while (true) {
 		          if (!findPolicyCycles()) break;
 		          contractPolicyGraph(comp);
 		          findPolicyCycle();
 		          if (!computeNodeDistances()) break;
+		        }
 		        // Update the best cycle (global minimum mean cycle)
 		        if ( !_best_found || (_curr_found &&
 		             _curr_length * _best_size < _best_length * _curr_size) ) {
 		          _best_found = true;
 		          _best_length = _curr_length;
 		          _best_size = _curr_size;
 		          _best_node = _curr_node;
+		        }
+		      }
-		      return _cycle_found;
+		      return _best_found;
+		    }
 		    /// \brief Find a minimum mean directed cycle.
 		    ///
 		    /// This function finds a directed cycle of minimum mean length
 		    /// in the digraph using the data computed by findMinMean().
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \pre \ref findMinMean() must be called before using this function.
 		    bool findCycle() {
 		      if (!_cycle_found) return false;
 		      _cycle_path->addBack(_policy[_cycle_node]);
 		      for ( Node v = _cycle_node;
 		            (v = _gr.target(_policy[v])) != _cycle_node; ) {
 		      if (!_best_found) return false;
 		      _cycle_path->addBack(_policy[_best_node]);
 		      for ( Node v = _best_node;
 		            (v = _gr.target(_policy[v])) != _best_node; ) {
 		        _cycle_path->addBack(_policy[v]);
+		      }
 		      return true;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The algorithm should be executed before using them.
 		    /// @{
 		    /// \brief Return the total length of the found cycle.
 		    ///
 		    /// This function returns the total length of the found cycle.
 		    ///
-		    /// \pre \ref run() or \ref findCycle() must be called before
+		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    Value cycleLength() const {
-		      return _cycle_length;
+		      return _best_length;
+		    }
 		    /// \brief Return the number of arcs on the found cycle.
 		    ///
 		    /// This function returns the number of arcs on the found cycle.
 		    ///
-		    /// \pre \ref run() or \ref findCycle() must be called before
+		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    int cycleArcNum() const {
-		      return _cycle_size;
+		      return _best_size;
+		    }
 		    /// \brief Return the mean length of the found cycle.
 		    ///
 		    /// This function returns the mean length of the found cycle.
 		    ///
-		    /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
+		    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
 		    /// following code.
 		    /// \code
-		    ///   return double(mmc.cycleLength()) / mmc.cycleArcNum();
+		    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
 		    /// \endcode
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    double cycleMean() const {
-		      return double(_cycle_length) / _cycle_size;
+		      return static_cast<double>(_best_length) / _best_size;
+		    }
 		    /// \brief Return the found cycle.
 		    ///
 		    /// This function returns a const reference to the path structure
 		    /// storing the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findCycle() must be called before using
 		    /// this function.
 		    ///
 		    /// \sa cyclePath()
 		    const Path& cycle() const {
 		      return *_cycle_path;
+		    }
 		    ///@}
 		  private:
 		    // Initialize the internal data structures for the current strongly
 		    // connected component and create the policy graph.
 		    // The policy graph can be represented by the _policy map because
 		    // the out-degree of every node is 1.
 		    bool initCurrentComponent(int comp) {
 		      // Find the nodes of the current component
 		      _nodes.clear();
 		      for (NodeIt n(_gr); n != INVALID; ++n) {
-		        if (_comp[n] == comp) _nodes.push_back(n);
+		    // Initialize
 		    void init() {
 		      _tol.epsilon(1e-6);
 		      if (!_cycle_path) {
 		        _local_path = true;
 		        _cycle_path = new Path;
+		      }
 		      if (_nodes.size() <= 1) return false;
 		      // Find the arcs of the current component
 		      _arcs.clear();
 		      for (ArcIt e(_gr); e != INVALID; ++e) {
 		        if ( _comp[_gr.source(e)] == comp &&
 		             _comp[_gr.target(e)] == comp )
-		          _arcs.push_back(e);
+		      _queue.resize(countNodes(_gr));
 		      _best_found = false;
 		      _best_length = 0;
 		      _best_size = 1;
 		      _cycle_path->clear();
+		    }
 		    // Find strongly connected components and initialize _comp_nodes
 		    // and _in_arcs
 		    void findComponents() {
 		      _comp_num = stronglyConnectedComponents(_gr, _comp);
 		      _comp_nodes.resize(_comp_num);
 		      if (_comp_num == 1) {
 		        _comp_nodes[0].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          _comp_nodes[0].push_back(n);
 		          _in_arcs[n].clear();
 		          for (InArcIt a(_gr, n); a != INVALID; ++a) {
 		            _in_arcs[n].push_back(a);
+		          }
+		        }
 		      } else {
 		        for (int i = 0; i < _comp_num; ++i)
 		          _comp_nodes[i].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          int k = _comp[n];
 		          _comp_nodes[k].push_back(n);
 		          _in_arcs[n].clear();
 		          for (InArcIt a(_gr, n); a != INVALID; ++a) {
 		            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
+		          }
+		        }
+		      }
 		      // Initialize _reached, _dist, _policy maps
 		      for (int i = 0; i < int(_nodes.size()); ++i) {
 		        _reached[_nodes[i]] = false;
 		        _policy[_nodes[i]] = INVALID;
+		    }
 		    // Build the policy graph in the given strongly connected component
 		    // (the out-degree of every node is 1)
 		    bool buildPolicyGraph(int comp) {
 		      _nodes = &(_comp_nodes[comp]);
 		      if (_nodes->size() < 1 ||
 		          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
 		        return false;
+		      }
 		      Node u; Arc e;
 		      for (int j = 0; j < int(_arcs.size()); ++j) {
 		        e = _arcs[j];
 		        u = _gr.source(e);
 		        if (!_reached[u] || _length[e] < _dist[u]) {
 		          _dist[u] = _length[e];
 		          _policy[u] = e;
 		          _reached[u] = true;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _dist[(*_nodes)[i]] = std::numeric_limits<double>::max();
+		      }
 		      Node u, v;
 		      Arc e;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        v = (*_nodes)[i];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (_length[e] < _dist[u]) {
 		            _dist[u] = _length[e];
 		            _policy[u] = e;
+		          }
+		        }
+		      }
 		      return true;
+		    }
 		    // Find all cycles in the policy graph.
 		    // Set _cycle_found to true if a cycle is found and set
 		    // _cycle_length, _cycle_size, _cycle_node to represent the minimum
 		    // mean cycle in the policy graph.
 		    bool findPolicyCycles() {
 		      typename Digraph::template NodeMap<int> level(_gr, -1);
-		      bool curr_cycle_found = false;
+		    // Find the minimum mean cycle in the policy graph
 		    void findPolicyCycle() {
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _level[(*_nodes)[i]] = -1;
+		      }
 		      Value clength;
 		      int csize;
 		      int path_cnt = 0;
 		      Node u, v;
 		      // Searching for cycles
 		      for (int i = 0; i < int(_nodes.size()); ++i) {
 		        if (level[_nodes[i]] < 0) {
 		          u = _nodes[i];
 		          level[u] = path_cnt;
 		          while (level[u = _gr.target(_policy[u])] < 0)
 		            level[u] = path_cnt;
 		          if (level[u] == path_cnt) {
 		            // A cycle is found
 		            curr_cycle_found = true;
 		            clength = _length[_policy[u]];
 		            csize = 1;
 		            for (v = u; (v = _gr.target(_policy[v])) != u; ) {
 		              clength += _length[_policy[v]];
 		              ++csize;
+		            }
 		            if ( !_cycle_found ||
 		                 clength * _cycle_size < _cycle_length * csize ) {
 		              _cycle_found = true;
 		              _cycle_length = clength;
 		              _cycle_size = csize;
 		              _cycle_node = u;
+		            }
+		      _curr_found = false;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        u = (*_nodes)[i];
 		        if (_level[u] >= 0) continue;
 		        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
 		          _level[u] = i;
+		        }
 		        if (_level[u] == i) {
 		          // A cycle is found
 		          clength = _length[_policy[u]];
 		          csize = 1;
 		          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
 		            clength += _length[_policy[v]];
 		            ++csize;
+		          }
 		          ++path_cnt;
+		        }
+		      }
 		      return curr_cycle_found;
+		    }
 		    // Contract the policy graph to be connected by cutting all cycles
 		    // except for the main cycle (i.e. the minimum mean cycle).
 		    void contractPolicyGraph(int comp) {
 		      // Find the component of the main cycle using reverse BFS search
 		      typename Digraph::template NodeMap<int> found(_gr, false);
 		      std::deque<Node> queue;
 		      queue.push_back(_cycle_node);
 		      found[_cycle_node] = true;
 		      Node u, v;
 		      while (!queue.empty()) {
 		        v = queue.front(); queue.pop_front();
 		        for (InArcIt e(_gr, v); e != INVALID; ++e) {
 		          u = _gr.source(e);
 		          if (_policy[u] == e && !found[u]) {
 		            found[u] = true;
 		            queue.push_back(u);
+		          }
+		        }
+		      }
 		      // Connect all other nodes to this component using reverse BFS search
 		      queue.clear();
 		      for (int i = 0; i < int(_nodes.size()); ++i)
 		        if (found[_nodes[i]]) queue.push_back(_nodes[i]);
 		      int found_cnt = queue.size();
 		      while (found_cnt < int(_nodes.size())) {
 		        v = queue.front(); queue.pop_front();
 		        for (InArcIt e(_gr, v); e != INVALID; ++e) {
 		          u = _gr.source(e);
 		          if (_comp[u] == comp && !found[u]) {
 		            found[u] = true;
 		            ++found_cnt;
 		            _policy[u] = e;
-		            queue.push_back(u);
+		          if ( !_curr_found ||
 		               (clength * _curr_size < _curr_length * csize) ) {
 		            _curr_found = true;
 		            _curr_length = clength;
 		            _curr_size = csize;
 		            _curr_node = u;
+		          }
+		        }
+		      }
+		    }
 		    // Compute node distances in the policy graph and update the
 		    // policy graph if the node distances can be improved.
 		    // Contract the policy graph and compute node distances
 		    bool computeNodeDistances() {
 		      // Compute node distances using reverse BFS search
 		      double cycle_mean = double(_cycle_length) / _cycle_size;
 		      typename Digraph::template NodeMap<int> found(_gr, false);
 		      std::deque<Node> queue;
 		      queue.push_back(_cycle_node);
 		      found[_cycle_node] = true;
-		      _dist[_cycle_node] = 0;
+		      // Find the component of the main cycle and compute node distances
 		      // using reverse BFS
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _reached[(*_nodes)[i]] = false;
+		      }
 		      double curr_mean = double(_curr_length) / _curr_size;
 		      _qfront = _qback = 0;
 		      _queue[0] = _curr_node;
 		      _reached[_curr_node] = true;
 		      _dist[_curr_node] = 0;
 		      Node u, v;
 		      while (!queue.empty()) {
 		        v = queue.front(); queue.pop_front();
-		        for (InArcIt e(_gr, v); e != INVALID; ++e) {
+		      Arc e;
 		      while (_qfront <= _qback) {
 		        v = _queue[_qfront++];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (_policy[u] == e && !found[u]) {
 		            found[u] = true;
 		            _dist[u] = _dist[v] + _length[e] - cycle_mean;
 		            queue.push_back(u);
 		          if (_policy[u] == e && !_reached[u]) {
 		            _reached[u] = true;
 		            _dist[u] = _dist[v] + _length[e] - curr_mean;
 		            _queue[++_qback] = u;
+		          }
+		        }
+		      }
-		      // Improving node distances
 		      // Connect all other nodes to this component and compute node
 		      // distances using reverse BFS
 		      _qfront = 0;
 		      while (_qback < int(_nodes->size())-1) {
 		        v = _queue[_qfront++];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (!_reached[u]) {
 		            _reached[u] = true;
 		            _policy[u] = e;
 		            _dist[u] = _dist[v] + _length[e] - curr_mean;
 		            _queue[++_qback] = u;
+		          }
+		        }
+		      }
 		      // Improve node distances
 		      bool improved = false;
 		      for (int j = 0; j < int(_arcs.size()); ++j) {
 		        Arc e = _arcs[j];
 		        u = _gr.source(e); v = _gr.target(e);
 		        double delta = _dist[v] + _length[e] - cycle_mean;
 		        if (_tol.less(delta, _dist[u])) {
 		          improved = true;
 		          _dist[u] = delta;
 		          _policy[u] = e;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        v = (*_nodes)[i];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          double delta = _dist[v] + _length[e] - curr_mean;
 		          if (_tol.less(delta, _dist[u])) {
 		            _dist[u] = delta;
 		            _policy[u] = e;
 		            improved = true;
+		          }
+		        }
+		      }
 		      return improved;
+		    }
 		  }; //class MinMeanCycle
 		  ///@}
 		} //namespace lemon
 		#endif //LEMON_MIN_MEAN_CYCLE_H

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