alpar@2409: /* -*- C++ -*-
alpar@2409:  *
alpar@2409:  * This file is a part of LEMON, a generic C++ optimization library
alpar@2409:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@2409:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@2409:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@2409:  *
alpar@2409:  * Permission to use, modify and distribute this software is granted
alpar@2409:  * provided that this copyright notice appears in all copies. For
alpar@2409:  * precise terms see the accompanying LICENSE file.
alpar@2409:  *
alpar@2409:  * This software is provided "AS IS" with no warranty of any kind,
alpar@2409:  * express or implied, and with no claim as to its suitability for any
alpar@2409:  * purpose.
alpar@2409:  *
alpar@2409:  */
alpar@2409: 
alpar@2409: #ifndef LEMON_MIN_MEAN_CYCLE_H
alpar@2409: #define LEMON_MIN_MEAN_CYCLE_H
alpar@2409: 
deba@2529: /// \ingroup shortest_path
alpar@2409: ///
deba@2437: /// \file
kpeter@2555: /// \brief Howard's algorithm for finding a minimum mean directed cycle.
alpar@2409: 
kpeter@2509: #include <vector>
alpar@2409: #include <lemon/graph_utils.h>
alpar@2409: #include <lemon/path.h>
kpeter@2555: #include <lemon/tolerance.h>
kpeter@2583: #include <lemon/topology.h>
alpar@2409: 
alpar@2409: namespace lemon {
alpar@2409: 
deba@2529:   /// \addtogroup shortest_path
alpar@2409:   /// @{
alpar@2409: 
kpeter@2555:   /// \brief Implementation of Howard's algorithm for finding a minimum
kpeter@2555:   /// mean directed cycle.
alpar@2409:   ///
kpeter@2555:   /// \ref MinMeanCycle implements Howard's algorithm for finding a
kpeter@2555:   /// minimum mean directed cycle.
alpar@2409:   ///
kpeter@2583:   /// \tparam Graph The directed graph type the algorithm runs on.
kpeter@2583:   /// \tparam LengthMap The type of the length (cost) map.
alpar@2409:   ///
kpeter@2555:   /// \warning \c LengthMap::Value must be convertible to \c double.
kpeter@2555:   ///
alpar@2409:   /// \author Peter Kovacs
alpar@2409: 
kpeter@2555:   template < typename Graph,
kpeter@2555:              typename LengthMap = typename Graph::template EdgeMap<int> >
alpar@2409:   class MinMeanCycle
alpar@2409:   {
kpeter@2555:     GRAPH_TYPEDEFS(typename Graph);
alpar@2409: 
alpar@2409:     typedef typename LengthMap::Value Length;
deba@2618:     typedef lemon::Path<Graph> Path;
alpar@2409: 
kpeter@2583:   private:
deba@2413: 
kpeter@2583:     // The directed graph the algorithm runs on
kpeter@2555:     const Graph &_graph;
kpeter@2583:     // The length of the edges
kpeter@2555:     const LengthMap &_length;
deba@2413: 
kpeter@2583:     // The total length of the found cycle
kpeter@2555:     Length _cycle_length;
kpeter@2583:     // The number of edges on the found cycle
kpeter@2555:     int _cycle_size;
kpeter@2583:     // The found cycle
kpeter@2555:     Path *_cycle_path;
deba@2413: 
kpeter@2555:     bool _local_path;
kpeter@2555:     bool _cycle_found;
kpeter@2555:     Node _cycle_node;
alpar@2409: 
kpeter@2583:     typename Graph::template NodeMap<bool> _reached;
kpeter@2583:     typename Graph::template NodeMap<double> _dist;
kpeter@2583:     typename Graph::template NodeMap<Edge> _policy;
kpeter@2583: 
kpeter@2555:     typename Graph::template NodeMap<int> _component;
kpeter@2555:     int _component_num;
deba@2437: 
kpeter@2555:     std::vector<Node> _nodes;
kpeter@2555:     std::vector<Edge> _edges;
kpeter@2555:     Tolerance<double> _tolerance;
deba@2437: 
kpeter@2555:   public:
alpar@2409: 
alpar@2409:     /// \brief The constructor of the class.
alpar@2409:     ///
alpar@2409:     /// The constructor of the class.
alpar@2409:     ///
kpeter@2555:     /// \param graph The directed graph the algorithm runs on.
kpeter@2555:     /// \param length The length (cost) of the edges.
kpeter@2555:     MinMeanCycle( const Graph &graph,
kpeter@2555:                   const LengthMap &length ) :
kpeter@2583:       _graph(graph), _length(length), _cycle_length(0), _cycle_size(-1),
kpeter@2583:       _cycle_path(NULL), _local_path(false), _reached(graph),
kpeter@2583:       _dist(graph), _policy(graph), _component(graph)
kpeter@2583:     {}
alpar@2409: 
kpeter@2555:     /// The destructor of the class.
deba@2437:     ~MinMeanCycle() {
kpeter@2555:       if (_local_path) delete _cycle_path;
alpar@2409:     }
alpar@2409: 
kpeter@2583:     /// \brief Sets the \ref Path "path" structure for storing the found
kpeter@2583:     /// cycle.
kpeter@2583:     ///
kpeter@2583:     /// Sets an external \ref Path "path" structure for storing the
kpeter@2583:     /// found cycle.
kpeter@2583:     ///
kpeter@2583:     /// If you don't call this function before calling \ref run() or
kpeter@2583:     /// \ref init(), it will allocate a local \ref Path "path"
kpeter@2583:     /// structure.
kpeter@2583:     /// The destuctor deallocates this automatically allocated map,
kpeter@2583:     /// of course.
kpeter@2583:     ///
kpeter@2583:     /// \note The algorithm calls only the \ref lemon::Path::addBack()
kpeter@2583:     /// "addBack()" function of the given \ref Path "path" structure.
kpeter@2583:     ///
kpeter@2583:     /// \return <tt>(*this)</tt>
kpeter@2583:     ///
kpeter@2583:     /// \sa cycle()
kpeter@2583:     MinMeanCycle& cyclePath(Path &path) {
kpeter@2583:       if (_local_path) {
kpeter@2583:         delete _cycle_path;
kpeter@2583:         _local_path = false;
alpar@2409:       }
kpeter@2583:       _cycle_path = &path;
kpeter@2583:       return *this;
kpeter@2555:     }
kpeter@2555: 
kpeter@2583:     /// \name Execution control
kpeter@2588:     /// The simplest way to execute the algorithm is to call the run()
kpeter@2588:     /// function.
kpeter@2583:     /// \n
kpeter@2583:     /// If you only need the minimum mean value, you may call init()
kpeter@2583:     /// and findMinMean().
kpeter@2583:     /// \n
kpeter@2583:     /// If you would like to run the algorithm again (e.g. the
kpeter@2583:     /// underlaying graph and/or the edge costs were modified), you may
kpeter@2583:     /// not create a new instance of the class, rather call reset(),
kpeter@2583:     /// findMinMean(), and findCycle() instead.
kpeter@2555: 
kpeter@2583:     /// @{
deba@2437: 
alpar@2409:     /// \brief Runs the algorithm.
alpar@2409:     ///
alpar@2409:     /// Runs the algorithm.
alpar@2409:     ///
kpeter@2555:     /// \return Returns \c true if a directed cycle exists in the graph.
deba@2413:     ///
kpeter@2555:     /// \note Apart from the return value, <tt>mmc.run()</tt> is just a
kpeter@2517:     /// shortcut of the following code.
deba@2413:     /// \code
kpeter@2555:     ///   mmc.init();
kpeter@2555:     ///   mmc.findMinMean();
kpeter@2555:     ///   mmc.findCycle();
deba@2413:     /// \endcode
alpar@2409:     bool run() {
alpar@2409:       init();
kpeter@2555:       return findMinMean() && findCycle();
deba@2413:     }
deba@2437: 
deba@2413:     /// \brief Initializes the internal data structures.
kpeter@2517:     ///
kpeter@2517:     /// Initializes the internal data structures.
kpeter@2517:     ///
kpeter@2517:     /// \sa reset()
deba@2413:     void init() {
kpeter@2583:       _tolerance.epsilon(1e-6);
kpeter@2555:       if (!_cycle_path) {
kpeter@2555:         _local_path = true;
kpeter@2555:         _cycle_path = new Path;
deba@2413:       }
kpeter@2555:       _cycle_found = false;
kpeter@2555:       _component_num = stronglyConnectedComponents(_graph, _component);
deba@2413:     }
deba@2413: 
deba@2413:     /// \brief Resets the internal data structures.
deba@2413:     ///
deba@2437:     /// Resets the internal data structures so that \ref findMinMean()
deba@2437:     /// and \ref findCycle() can be called again (e.g. when the
deba@2413:     /// underlaying graph has been modified).
kpeter@2517:     ///
kpeter@2517:     /// \sa init()
deba@2413:     void reset() {
kpeter@2555:       if (_cycle_path) _cycle_path->clear();
kpeter@2555:       _cycle_found = false;
kpeter@2555:       _component_num = stronglyConnectedComponents(_graph, _component);
kpeter@2555:     }
kpeter@2555: 
kpeter@2555:     /// \brief Finds the minimum cycle mean length in the graph.
kpeter@2555:     ///
kpeter@2555:     /// Computes all the required data and finds the minimum cycle mean
kpeter@2555:     /// length in the graph.
kpeter@2555:     ///
kpeter@2555:     /// \return Returns \c true if a directed cycle exists in the graph.
kpeter@2555:     ///
kpeter@2555:     /// \pre \ref init() must be called before using this function.
kpeter@2555:     bool findMinMean() {
kpeter@2555:       // Finding the minimum mean cycle in the components
kpeter@2555:       for (int comp = 0; comp < _component_num; ++comp) {
kpeter@2555:         if (!initCurrentComponent(comp)) continue;
kpeter@2555:         while (true) {
kpeter@2583:           if (!findPolicyCycles()) break;
kpeter@2555:           contractPolicyGraph(comp);
kpeter@2583:           if (!computeNodeDistances(comp)) break;
kpeter@2555:         }
kpeter@2555:       }
kpeter@2583:       return _cycle_found;
kpeter@2555:     }
kpeter@2555: 
kpeter@2555:     /// \brief Finds a critical (minimum mean) directed cycle.
kpeter@2555:     ///
kpeter@2555:     /// Finds a critical (minimum mean) directed cycle using the data
kpeter@2555:     /// computed in the \ref findMinMean() function.
kpeter@2555:     ///
kpeter@2555:     /// \return Returns \c true if a directed cycle exists in the graph.
kpeter@2555:     ///
kpeter@2555:     /// \pre \ref init() and \ref findMinMean() must be called before
kpeter@2555:     /// using this function.
kpeter@2555:     bool findCycle() {
kpeter@2555:       if (!_cycle_found) return false;
kpeter@2555:       _cycle_path->addBack(_policy[_cycle_node]);
kpeter@2555:       for ( Node v = _cycle_node;
kpeter@2555:             (v = _graph.target(_policy[v])) != _cycle_node; ) {
kpeter@2555:         _cycle_path->addBack(_policy[v]);
kpeter@2555:       }
kpeter@2555:       return true;
deba@2413:     }
kpeter@2620: 
kpeter@2583:     /// @}
deba@2437: 
kpeter@2583:     /// \name Query Functions
kpeter@2583:     /// The result of the algorithm can be obtained using these
kpeter@2583:     /// functions.
kpeter@2588:     /// \n The algorithm should be executed before using them.
kpeter@2583: 
kpeter@2583:     /// @{
kpeter@2620: 
deba@2413:     /// \brief Returns the total length of the found cycle.
deba@2413:     ///
deba@2413:     /// Returns the total length of the found cycle.
alpar@2409:     ///
kpeter@2555:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@2555:     /// using this function.
deba@2437:     Length cycleLength() const {
kpeter@2555:       return _cycle_length;
alpar@2409:     }
deba@2437: 
kpeter@2555:     /// \brief Returns the number of edges on the found cycle.
alpar@2409:     ///
kpeter@2555:     /// Returns the number of edges on the found cycle.
alpar@2409:     ///
kpeter@2555:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@2555:     /// using this function.
deba@2437:     int cycleEdgeNum() const {
kpeter@2555:       return _cycle_size;
alpar@2409:     }
deba@2437: 
deba@2413:     /// \brief Returns the mean length of the found cycle.
alpar@2409:     ///
deba@2413:     /// Returns the mean length of the found cycle.
alpar@2409:     ///
kpeter@2517:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@2517:     /// using this function.
alpar@2409:     ///
kpeter@2555:     /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
kpeter@2555:     /// following code.
deba@2413:     /// \code
kpeter@2555:     ///   return double(mmc.cycleLength()) / mmc.cycleEdgeNum();
deba@2413:     /// \endcode
kpeter@2555:     double cycleMean() const {
kpeter@2583:       return double(_cycle_length) / _cycle_size;
alpar@2409:     }
alpar@2409: 
kpeter@2555:     /// \brief Returns a const reference to the \ref Path "path"
kpeter@2555:     /// structure storing the found cycle.
alpar@2409:     ///
kpeter@2555:     /// Returns a const reference to the \ref Path "path"
kpeter@2555:     /// structure storing the found cycle.
alpar@2409:     ///
kpeter@2555:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@2555:     /// this function.
alpar@2409:     ///
kpeter@2555:     /// \sa cyclePath()
deba@2437:     const Path& cycle() const {
kpeter@2555:       return *_cycle_path;
alpar@2409:     }
kpeter@2620: 
kpeter@2583:     ///@}
kpeter@2620: 
kpeter@2583:   private:
deba@2437: 
kpeter@2583:     // Initializes the internal data structures for the current strongly
kpeter@2583:     // connected component and creating the policy graph.
kpeter@2583:     // The policy graph can be represented by the _policy map because
kpeter@2583:     // the out degree of every node is 1.
kpeter@2583:     bool initCurrentComponent(int comp) {
kpeter@2583:       // Finding the nodes of the current component
kpeter@2583:       _nodes.clear();
kpeter@2583:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2583:         if (_component[n] == comp) _nodes.push_back(n);
alpar@2409:       }
kpeter@2583:       if (_nodes.size() <= 1) return false;
kpeter@2583:       // Finding the edges of the current component
kpeter@2583:       _edges.clear();
kpeter@2583:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2583:         if ( _component[_graph.source(e)] == comp &&
kpeter@2583:              _component[_graph.target(e)] == comp )
kpeter@2583:           _edges.push_back(e);
kpeter@2583:       }
kpeter@2583:       // Initializing _reached, _dist, _policy maps
kpeter@2583:       for (int i = 0; i < int(_nodes.size()); ++i) {
kpeter@2583:         _reached[_nodes[i]] = false;
kpeter@2583:         _policy[_nodes[i]] = INVALID;
kpeter@2583:       }
kpeter@2583:       Node u; Edge e;
kpeter@2583:       for (int j = 0; j < int(_edges.size()); ++j) {
kpeter@2583:         e = _edges[j];
kpeter@2583:         u = _graph.source(e);
kpeter@2583:         if (!_reached[u] || _length[e] < _dist[u]) {
kpeter@2583:           _dist[u] = _length[e];
kpeter@2583:           _policy[u] = e;
kpeter@2583:           _reached[u] = true;
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:       return true;
kpeter@2583:     }
kpeter@2583: 
kpeter@2583:     // Finds all cycles in the policy graph.
kpeter@2583:     // Sets _cycle_found to true if a cycle is found and sets
kpeter@2583:     // _cycle_length, _cycle_size, _cycle_node to represent the minimum
kpeter@2583:     // mean cycle in the policy graph.
kpeter@2583:     bool findPolicyCycles() {
kpeter@2583:       typename Graph::template NodeMap<int> level(_graph, -1);
kpeter@2583:       bool curr_cycle_found = false;
kpeter@2583:       Length clength;
kpeter@2583:       int csize;
kpeter@2583:       int path_cnt = 0;
kpeter@2583:       Node u, v;
kpeter@2583:       // Searching for cycles
kpeter@2583:       for (int i = 0; i < int(_nodes.size()); ++i) {
kpeter@2583:         if (level[_nodes[i]] < 0) {
kpeter@2583:           u = _nodes[i];
kpeter@2583:           level[u] = path_cnt;
kpeter@2583:           while (level[u = _graph.target(_policy[u])] < 0)
kpeter@2583:             level[u] = path_cnt;
kpeter@2583:           if (level[u] == path_cnt) {
kpeter@2583:             // A cycle is found
kpeter@2583:             curr_cycle_found = true;
kpeter@2583:             clength = _length[_policy[u]];
kpeter@2583:             csize = 1;
kpeter@2583:             for (v = u; (v = _graph.target(_policy[v])) != u; ) {
kpeter@2583:               clength += _length[_policy[v]];
kpeter@2583:               ++csize;
kpeter@2583:             }
kpeter@2583:             if ( !_cycle_found ||
kpeter@2583:                  clength * _cycle_size < _cycle_length * csize ) {
kpeter@2583:               _cycle_found = true;
kpeter@2583:               _cycle_length = clength;
kpeter@2583:               _cycle_size = csize;
kpeter@2583:               _cycle_node = u;
kpeter@2583:             }
kpeter@2583:           }
kpeter@2583:           ++path_cnt;
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:       return curr_cycle_found;
kpeter@2583:     }
kpeter@2583: 
kpeter@2583:     // Contracts the policy graph to be connected by cutting all cycles
kpeter@2583:     // except for the main cycle (i.e. the minimum mean cycle).
kpeter@2583:     void contractPolicyGraph(int comp) {
kpeter@2583:       // Finding the component of the main cycle using
kpeter@2583:       // reverse BFS search
kpeter@2583:       typename Graph::template NodeMap<int> found(_graph, false);
kpeter@2583:       std::deque<Node> queue;
kpeter@2583:       queue.push_back(_cycle_node);
kpeter@2583:       found[_cycle_node] = true;
kpeter@2583:       Node u, v;
kpeter@2583:       while (!queue.empty()) {
kpeter@2583:         v = queue.front(); queue.pop_front();
kpeter@2583:         for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
kpeter@2583:           u = _graph.source(e);
kpeter@2583:           if (_component[u] == comp && !found[u] && _policy[u] == e) {
kpeter@2583:             found[u] = true;
kpeter@2583:             queue.push_back(u);
kpeter@2583:           }
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:       // Connecting all other nodes to this component using
kpeter@2583:       // reverse BFS search
kpeter@2583:       queue.clear();
kpeter@2583:       for (int i = 0; i < int(_nodes.size()); ++i)
kpeter@2583:         if (found[_nodes[i]]) queue.push_back(_nodes[i]);
kpeter@2583:       int found_cnt = queue.size();
kpeter@2583:       while (found_cnt < int(_nodes.size()) && !queue.empty()) {
kpeter@2583:         v = queue.front(); queue.pop_front();
kpeter@2583:         for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
kpeter@2583:           u = _graph.source(e);
kpeter@2583:           if (_component[u] == comp && !found[u]) {
kpeter@2583:             found[u] = true;
kpeter@2583:             ++found_cnt;
kpeter@2583:             _policy[u] = e;
kpeter@2583:             queue.push_back(u);
kpeter@2583:           }
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:     }
kpeter@2583: 
kpeter@2583:     // Computes node distances in the policy graph and updates the
kpeter@2583:     // policy graph if the node distances can be improved.
kpeter@2583:     bool computeNodeDistances(int comp) {
kpeter@2583:       // Computing node distances using reverse BFS search
kpeter@2583:       double cycle_mean = double(_cycle_length) / _cycle_size;
kpeter@2583:       typename Graph::template NodeMap<int> found(_graph, false);
kpeter@2583:       std::deque<Node> queue;
kpeter@2583:       queue.push_back(_cycle_node);
kpeter@2583:       found[_cycle_node] = true;
kpeter@2583:       _dist[_cycle_node] = 0;
kpeter@2583:       Node u, v;
kpeter@2583:       while (!queue.empty()) {
kpeter@2583:         v = queue.front(); queue.pop_front();
kpeter@2583:         for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
kpeter@2583:           u = _graph.source(e);
kpeter@2583:           if (_component[u] == comp && !found[u] && _policy[u] == e) {
kpeter@2583:             found[u] = true;
kpeter@2583:             _dist[u] = _dist[v] + _length[e] - cycle_mean;
kpeter@2583:             queue.push_back(u);
kpeter@2583:           }
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:       // Improving node distances
kpeter@2583:       bool improved = false;
kpeter@2583:       for (int j = 0; j < int(_edges.size()); ++j) {
kpeter@2583:         Edge e = _edges[j];
kpeter@2583:         u = _graph.source(e); v = _graph.target(e);
kpeter@2583:         double delta = _dist[v] + _length[e] - cycle_mean;
kpeter@2583:         if (_tolerance.less(delta, _dist[u])) {
kpeter@2583:           improved = true;
kpeter@2583:           _dist[u] = delta;
kpeter@2583:           _policy[u] = e;
kpeter@2583:         }
kpeter@2583:       }
kpeter@2583:       return improved;
alpar@2409:     }
alpar@2409: 
alpar@2409:   }; //class MinMeanCycle
alpar@2409: 
alpar@2409:   ///@}
alpar@2409: 
alpar@2409: } //namespace lemon
alpar@2409: 
alpar@2409: #endif //LEMON_MIN_MEAN_CYCLE_H