kpeter@758: /* -*- C++ -*-
kpeter@758:  *
kpeter@758:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@758:  *
kpeter@758:  * Copyright (C) 2003-2008
kpeter@758:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@758:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@758:  *
kpeter@758:  * Permission to use, modify and distribute this software is granted
kpeter@758:  * provided that this copyright notice appears in all copies. For
kpeter@758:  * precise terms see the accompanying LICENSE file.
kpeter@758:  *
kpeter@758:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@758:  * express or implied, and with no claim as to its suitability for any
kpeter@758:  * purpose.
kpeter@758:  *
kpeter@758:  */
kpeter@758: 
kpeter@758: #ifndef LEMON_MIN_MEAN_CYCLE_H
kpeter@758: #define LEMON_MIN_MEAN_CYCLE_H
kpeter@758: 
kpeter@758: /// \ingroup shortest_path
kpeter@758: ///
kpeter@758: /// \file
kpeter@758: /// \brief Howard's algorithm for finding a minimum mean cycle.
kpeter@758: 
kpeter@758: #include <vector>
kpeter@758: #include <lemon/core.h>
kpeter@758: #include <lemon/path.h>
kpeter@758: #include <lemon/tolerance.h>
kpeter@758: #include <lemon/connectivity.h>
kpeter@758: 
kpeter@758: namespace lemon {
kpeter@758: 
kpeter@758:   /// \addtogroup shortest_path
kpeter@758:   /// @{
kpeter@758: 
kpeter@758:   /// \brief Implementation of Howard's algorithm for finding a minimum
kpeter@758:   /// mean cycle.
kpeter@758:   ///
kpeter@758:   /// \ref MinMeanCycle implements Howard's algorithm for finding a
kpeter@758:   /// directed cycle of minimum mean length (cost) in a digraph.
kpeter@758:   ///
kpeter@758:   /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@758:   /// \tparam LEN The type of the length map. The default
kpeter@758:   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@758:   ///
kpeter@758:   /// \warning \c LEN::Value must be convertible to \c double.
kpeter@758: #ifdef DOXYGEN
kpeter@758:   template <typename GR, typename LEN>
kpeter@758: #else
kpeter@758:   template < typename GR,
kpeter@758:              typename LEN = typename GR::template ArcMap<int> >
kpeter@758: #endif
kpeter@758:   class MinMeanCycle
kpeter@758:   {
kpeter@758:   public:
kpeter@758:   
kpeter@758:     /// The type of the digraph the algorithm runs on
kpeter@758:     typedef GR Digraph;
kpeter@758:     /// The type of the length map
kpeter@758:     typedef LEN LengthMap;
kpeter@758:     /// The type of the arc lengths
kpeter@758:     typedef typename LengthMap::Value Value;
kpeter@758:     /// The type of the paths
kpeter@758:     typedef lemon::Path<Digraph> Path;
kpeter@758: 
kpeter@758:   private:
kpeter@758: 
kpeter@758:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@758:   
kpeter@758:     // The digraph the algorithm runs on
kpeter@758:     const Digraph &_gr;
kpeter@758:     // The length of the arcs
kpeter@758:     const LengthMap &_length;
kpeter@758: 
kpeter@758:     // The total length of the found cycle
kpeter@758:     Value _cycle_length;
kpeter@758:     // The number of arcs on the found cycle
kpeter@758:     int _cycle_size;
kpeter@758:     // The found cycle
kpeter@758:     Path *_cycle_path;
kpeter@758: 
kpeter@758:     bool _local_path;
kpeter@758:     bool _cycle_found;
kpeter@758:     Node _cycle_node;
kpeter@758: 
kpeter@758:     typename Digraph::template NodeMap<bool> _reached;
kpeter@758:     typename Digraph::template NodeMap<double> _dist;
kpeter@758:     typename Digraph::template NodeMap<Arc> _policy;
kpeter@758: 
kpeter@758:     typename Digraph::template NodeMap<int> _comp;
kpeter@758:     int _comp_num;
kpeter@758: 
kpeter@758:     std::vector<Node> _nodes;
kpeter@758:     std::vector<Arc> _arcs;
kpeter@758:     Tolerance<double> _tol;
kpeter@758: 
kpeter@758:   public:
kpeter@758: 
kpeter@758:     /// \brief Constructor.
kpeter@758:     ///
kpeter@758:     /// The constructor of the class.
kpeter@758:     ///
kpeter@758:     /// \param digraph The digraph the algorithm runs on.
kpeter@758:     /// \param length The lengths (costs) of the arcs.
kpeter@758:     MinMeanCycle( const Digraph &digraph,
kpeter@758:                   const LengthMap &length ) :
kpeter@758:       _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
kpeter@758:       _cycle_path(NULL), _local_path(false), _reached(digraph),
kpeter@758:       _dist(digraph), _policy(digraph), _comp(digraph)
kpeter@758:     {}
kpeter@758: 
kpeter@758:     /// Destructor.
kpeter@758:     ~MinMeanCycle() {
kpeter@758:       if (_local_path) delete _cycle_path;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Set the path structure for storing the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function sets an external path structure for storing the
kpeter@758:     /// found cycle.
kpeter@758:     ///
kpeter@758:     /// If you don't call this function before calling \ref run() or
kpeter@758:     /// \ref init(), it will allocate a local \ref Path "path"
kpeter@758:     /// structure. The destuctor deallocates this automatically
kpeter@758:     /// allocated object, of course.
kpeter@758:     ///
kpeter@758:     /// \note The algorithm calls only the \ref lemon::Path::addBack()
kpeter@758:     /// "addBack()" function of the given path structure.
kpeter@758:     ///
kpeter@758:     /// \return <tt>(*this)</tt>
kpeter@758:     ///
kpeter@758:     /// \sa cycle()
kpeter@758:     MinMeanCycle& cyclePath(Path &path) {
kpeter@758:       if (_local_path) {
kpeter@758:         delete _cycle_path;
kpeter@758:         _local_path = false;
kpeter@758:       }
kpeter@758:       _cycle_path = &path;
kpeter@758:       return *this;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \name Execution control
kpeter@758:     /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@758:     /// function.\n
kpeter@758:     /// If you only need the minimum mean length, you may call \ref init()
kpeter@758:     /// and \ref findMinMean().
kpeter@758:     /// If you would like to run the algorithm again (e.g. the underlying
kpeter@758:     /// digraph and/or the arc lengths has been modified), you may not
kpeter@758:     /// create a new instance of the class, rather call \ref reset(),
kpeter@758:     /// \ref findMinMean() and \ref findCycle() instead.
kpeter@758: 
kpeter@758:     /// @{
kpeter@758: 
kpeter@758:     /// \brief Run the algorithm.
kpeter@758:     ///
kpeter@758:     /// This function runs the algorithm.
kpeter@758:     ///
kpeter@758:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@758:     ///
kpeter@758:     /// \note Apart from the return value, <tt>mmc.run()</tt> is just a
kpeter@758:     /// shortcut of the following code.
kpeter@758:     /// \code
kpeter@758:     ///   mmc.init();
kpeter@758:     ///   mmc.findMinMean();
kpeter@758:     ///   mmc.findCycle();
kpeter@758:     /// \endcode
kpeter@758:     bool run() {
kpeter@758:       init();
kpeter@758:       return findMinMean() && findCycle();
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Initialize the internal data structures.
kpeter@758:     ///
kpeter@758:     /// This function initializes the internal data structures.
kpeter@758:     ///
kpeter@758:     /// \sa reset()
kpeter@758:     void init() {
kpeter@758:       _tol.epsilon(1e-6);
kpeter@758:       if (!_cycle_path) {
kpeter@758:         _local_path = true;
kpeter@758:         _cycle_path = new Path;
kpeter@758:       }
kpeter@758:       _cycle_found = false;
kpeter@758:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Reset the internal data structures.
kpeter@758:     ///
kpeter@758:     /// This function resets the internal data structures so that
kpeter@758:     /// findMinMean() and findCycle() can be called again (e.g. when the
kpeter@758:     /// underlying digraph and/or the arc lengths has been modified).
kpeter@758:     ///
kpeter@758:     /// \sa init()
kpeter@758:     void reset() {
kpeter@758:       if (_cycle_path) _cycle_path->clear();
kpeter@758:       _cycle_found = false;
kpeter@758:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Find the minimum cycle mean.
kpeter@758:     ///
kpeter@758:     /// This function computes all the required data and finds the
kpeter@758:     /// minimum mean length of the directed cycles in the digraph.
kpeter@758:     ///
kpeter@758:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@758:     ///
kpeter@758:     /// \pre \ref init() must be called before using this function.
kpeter@758:     bool findMinMean() {
kpeter@758:       // Find the minimum cycle mean in the components
kpeter@758:       for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@758:         if (!initCurrentComponent(comp)) continue;
kpeter@758:         while (true) {
kpeter@758:           if (!findPolicyCycles()) break;
kpeter@758:           contractPolicyGraph(comp);
kpeter@758:           if (!computeNodeDistances()) break;
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return _cycle_found;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Find a minimum mean directed cycle.
kpeter@758:     ///
kpeter@758:     /// This function finds a directed cycle of minimum mean length
kpeter@758:     /// in the digraph using the data computed by findMinMean().
kpeter@758:     ///
kpeter@758:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@758:     ///
kpeter@758:     /// \pre \ref init() and \ref findMinMean() must be called before
kpeter@758:     /// using this function.
kpeter@758:     bool findCycle() {
kpeter@758:       if (!_cycle_found) return false;
kpeter@758:       _cycle_path->addBack(_policy[_cycle_node]);
kpeter@758:       for ( Node v = _cycle_node;
kpeter@758:             (v = _gr.target(_policy[v])) != _cycle_node; ) {
kpeter@758:         _cycle_path->addBack(_policy[v]);
kpeter@758:       }
kpeter@758:       return true;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// @}
kpeter@758: 
kpeter@758:     /// \name Query Functions
kpeter@758:     /// The result of the algorithm can be obtained using these
kpeter@758:     /// functions.\n
kpeter@758:     /// The algorithm should be executed before using them.
kpeter@758: 
kpeter@758:     /// @{
kpeter@758: 
kpeter@758:     /// \brief Return the total length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the total length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findCycle() must be called before
kpeter@758:     /// using this function.
kpeter@758:     Value cycleLength() const {
kpeter@758:       return _cycle_length;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the number of arcs on the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the number of arcs on the found cycle.
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findCycle() must be called before
kpeter@758:     /// using this function.
kpeter@758:     int cycleArcNum() const {
kpeter@758:       return _cycle_size;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the mean length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the mean length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
kpeter@758:     /// following code.
kpeter@758:     /// \code
kpeter@758:     ///   return double(mmc.cycleLength()) / mmc.cycleArcNum();
kpeter@758:     /// \endcode
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758:     /// using this function.
kpeter@758:     double cycleMean() const {
kpeter@758:       return double(_cycle_length) / _cycle_size;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns a const reference to the path structure
kpeter@758:     /// storing the found cycle.
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@758:     /// this function.
kpeter@758:     ///
kpeter@758:     /// \sa cyclePath()
kpeter@758:     const Path& cycle() const {
kpeter@758:       return *_cycle_path;
kpeter@758:     }
kpeter@758: 
kpeter@758:     ///@}
kpeter@758: 
kpeter@758:   private:
kpeter@758: 
kpeter@758:     // Initialize the internal data structures for the current strongly
kpeter@758:     // connected component and create the policy graph.
kpeter@758:     // The policy graph can be represented by the _policy map because
kpeter@758:     // the out-degree of every node is 1.
kpeter@758:     bool initCurrentComponent(int comp) {
kpeter@758:       // Find the nodes of the current component
kpeter@758:       _nodes.clear();
kpeter@758:       for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@758:         if (_comp[n] == comp) _nodes.push_back(n);
kpeter@758:       }
kpeter@758:       if (_nodes.size() <= 1) return false;
kpeter@758:       // Find the arcs of the current component
kpeter@758:       _arcs.clear();
kpeter@758:       for (ArcIt e(_gr); e != INVALID; ++e) {
kpeter@758:         if ( _comp[_gr.source(e)] == comp &&
kpeter@758:              _comp[_gr.target(e)] == comp )
kpeter@758:           _arcs.push_back(e);
kpeter@758:       }
kpeter@758:       // Initialize _reached, _dist, _policy maps
kpeter@758:       for (int i = 0; i < int(_nodes.size()); ++i) {
kpeter@758:         _reached[_nodes[i]] = false;
kpeter@758:         _policy[_nodes[i]] = INVALID;
kpeter@758:       }
kpeter@758:       Node u; Arc e;
kpeter@758:       for (int j = 0; j < int(_arcs.size()); ++j) {
kpeter@758:         e = _arcs[j];
kpeter@758:         u = _gr.source(e);
kpeter@758:         if (!_reached[u] || _length[e] < _dist[u]) {
kpeter@758:           _dist[u] = _length[e];
kpeter@758:           _policy[u] = e;
kpeter@758:           _reached[u] = true;
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return true;
kpeter@758:     }
kpeter@758: 
kpeter@758:     // Find all cycles in the policy graph.
kpeter@758:     // Set _cycle_found to true if a cycle is found and set
kpeter@758:     // _cycle_length, _cycle_size, _cycle_node to represent the minimum
kpeter@758:     // mean cycle in the policy graph.
kpeter@758:     bool findPolicyCycles() {
kpeter@758:       typename Digraph::template NodeMap<int> level(_gr, -1);
kpeter@758:       bool curr_cycle_found = false;
kpeter@758:       Value clength;
kpeter@758:       int csize;
kpeter@758:       int path_cnt = 0;
kpeter@758:       Node u, v;
kpeter@758:       // Searching for cycles
kpeter@758:       for (int i = 0; i < int(_nodes.size()); ++i) {
kpeter@758:         if (level[_nodes[i]] < 0) {
kpeter@758:           u = _nodes[i];
kpeter@758:           level[u] = path_cnt;
kpeter@758:           while (level[u = _gr.target(_policy[u])] < 0)
kpeter@758:             level[u] = path_cnt;
kpeter@758:           if (level[u] == path_cnt) {
kpeter@758:             // A cycle is found
kpeter@758:             curr_cycle_found = true;
kpeter@758:             clength = _length[_policy[u]];
kpeter@758:             csize = 1;
kpeter@758:             for (v = u; (v = _gr.target(_policy[v])) != u; ) {
kpeter@758:               clength += _length[_policy[v]];
kpeter@758:               ++csize;
kpeter@758:             }
kpeter@758:             if ( !_cycle_found ||
kpeter@758:                  clength * _cycle_size < _cycle_length * csize ) {
kpeter@758:               _cycle_found = true;
kpeter@758:               _cycle_length = clength;
kpeter@758:               _cycle_size = csize;
kpeter@758:               _cycle_node = u;
kpeter@758:             }
kpeter@758:           }
kpeter@758:           ++path_cnt;
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return curr_cycle_found;
kpeter@758:     }
kpeter@758: 
kpeter@758:     // Contract the policy graph to be connected by cutting all cycles
kpeter@758:     // except for the main cycle (i.e. the minimum mean cycle).
kpeter@758:     void contractPolicyGraph(int comp) {
kpeter@758:       // Find the component of the main cycle using reverse BFS search
kpeter@758:       typename Digraph::template NodeMap<int> found(_gr, false);
kpeter@758:       std::deque<Node> queue;
kpeter@758:       queue.push_back(_cycle_node);
kpeter@758:       found[_cycle_node] = true;
kpeter@758:       Node u, v;
kpeter@758:       while (!queue.empty()) {
kpeter@758:         v = queue.front(); queue.pop_front();
kpeter@758:         for (InArcIt e(_gr, v); e != INVALID; ++e) {
kpeter@758:           u = _gr.source(e);
kpeter@758:           if (_policy[u] == e && !found[u]) {
kpeter@758:             found[u] = true;
kpeter@758:             queue.push_back(u);
kpeter@758:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:       // Connect all other nodes to this component using reverse BFS search
kpeter@758:       queue.clear();
kpeter@758:       for (int i = 0; i < int(_nodes.size()); ++i)
kpeter@758:         if (found[_nodes[i]]) queue.push_back(_nodes[i]);
kpeter@758:       int found_cnt = queue.size();
kpeter@758:       while (found_cnt < int(_nodes.size())) {
kpeter@758:         v = queue.front(); queue.pop_front();
kpeter@758:         for (InArcIt e(_gr, v); e != INVALID; ++e) {
kpeter@758:           u = _gr.source(e);
kpeter@758:           if (_comp[u] == comp && !found[u]) {
kpeter@758:             found[u] = true;
kpeter@758:             ++found_cnt;
kpeter@758:             _policy[u] = e;
kpeter@758:             queue.push_back(u);
kpeter@758:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:     }
kpeter@758: 
kpeter@758:     // Compute node distances in the policy graph and update the
kpeter@758:     // policy graph if the node distances can be improved.
kpeter@758:     bool computeNodeDistances() {
kpeter@758:       // Compute node distances using reverse BFS search
kpeter@758:       double cycle_mean = double(_cycle_length) / _cycle_size;
kpeter@758:       typename Digraph::template NodeMap<int> found(_gr, false);
kpeter@758:       std::deque<Node> queue;
kpeter@758:       queue.push_back(_cycle_node);
kpeter@758:       found[_cycle_node] = true;
kpeter@758:       _dist[_cycle_node] = 0;
kpeter@758:       Node u, v;
kpeter@758:       while (!queue.empty()) {
kpeter@758:         v = queue.front(); queue.pop_front();
kpeter@758:         for (InArcIt e(_gr, v); e != INVALID; ++e) {
kpeter@758:           u = _gr.source(e);
kpeter@758:           if (_policy[u] == e && !found[u]) {
kpeter@758:             found[u] = true;
kpeter@758:             _dist[u] = _dist[v] + _length[e] - cycle_mean;
kpeter@758:             queue.push_back(u);
kpeter@758:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:       // Improving node distances
kpeter@758:       bool improved = false;
kpeter@758:       for (int j = 0; j < int(_arcs.size()); ++j) {
kpeter@758:         Arc e = _arcs[j];
kpeter@758:         u = _gr.source(e); v = _gr.target(e);
kpeter@758:         double delta = _dist[v] + _length[e] - cycle_mean;
kpeter@758:         if (_tol.less(delta, _dist[u])) {
kpeter@758:           improved = true;
kpeter@758:           _dist[u] = delta;
kpeter@758:           _policy[u] = e;
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return improved;
kpeter@758:     }
kpeter@758: 
kpeter@758:   }; //class MinMeanCycle
kpeter@758: 
kpeter@758:   ///@}
kpeter@758: 
kpeter@758: } //namespace lemon
kpeter@758: 
kpeter@758: #endif //LEMON_MIN_MEAN_CYCLE_H