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@764: #ifndef LEMON_HOWARD_H
kpeter@764: #define LEMON_HOWARD_H
kpeter@758:
kpeter@768: /// \ingroup min_mean_cycle
kpeter@758: ///
kpeter@758: /// \file
kpeter@758: /// \brief Howard's algorithm for finding a minimum mean cycle.
kpeter@758:
kpeter@758: #include <vector>
kpeter@763: #include <limits>
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@764: /// \brief Default traits class of Howard class.
kpeter@761: ///
kpeter@764: /// Default traits class of Howard class.
kpeter@761: /// \tparam GR The type of the digraph.
kpeter@761: /// \tparam LEN The type of the length map.
kpeter@761: /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@761: #ifdef DOXYGEN
kpeter@761: template <typename GR, typename LEN>
kpeter@761: #else
kpeter@761: template <typename GR, typename LEN,
kpeter@761: bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
kpeter@761: #endif
kpeter@764: struct HowardDefaultTraits
kpeter@761: {
kpeter@761: /// The type of the digraph
kpeter@761: typedef GR Digraph;
kpeter@761: /// The type of the length map
kpeter@761: typedef LEN LengthMap;
kpeter@761: /// The type of the arc lengths
kpeter@761: typedef typename LengthMap::Value Value;
kpeter@761:
kpeter@761: /// \brief The large value type used for internal computations
kpeter@761: ///
kpeter@761: /// The large value type used for internal computations.
kpeter@761: /// It is \c long \c long if the \c Value type is integer,
kpeter@761: /// otherwise it is \c double.
kpeter@761: /// \c Value must be convertible to \c LargeValue.
kpeter@761: typedef double LargeValue;
kpeter@761:
kpeter@761: /// The tolerance type used for internal computations
kpeter@761: typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@761:
kpeter@761: /// \brief The path type of the found cycles
kpeter@761: ///
kpeter@761: /// The path type of the found cycles.
kpeter@761: /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@761: /// and it must have an \c addBack() function.
kpeter@761: typedef lemon::Path<Digraph> Path;
kpeter@761: };
kpeter@761:
kpeter@761: // Default traits class for integer value types
kpeter@761: template <typename GR, typename LEN>
kpeter@764: struct HowardDefaultTraits<GR, LEN, true>
kpeter@761: {
kpeter@761: typedef GR Digraph;
kpeter@761: typedef LEN LengthMap;
kpeter@761: typedef typename LengthMap::Value Value;
kpeter@761: #ifdef LEMON_HAVE_LONG_LONG
kpeter@761: typedef long long LargeValue;
kpeter@761: #else
kpeter@761: typedef long LargeValue;
kpeter@761: #endif
kpeter@761: typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@761: typedef lemon::Path<Digraph> Path;
kpeter@761: };
kpeter@761:
kpeter@761:
kpeter@768: /// \addtogroup min_mean_cycle
kpeter@758: /// @{
kpeter@758:
kpeter@758: /// \brief Implementation of Howard's algorithm for finding a minimum
kpeter@758: /// mean cycle.
kpeter@758: ///
kpeter@764: /// This class implements Howard's policy iteration algorithm for finding
kpeter@771: /// a directed cycle of minimum mean length (cost) in a digraph
kpeter@771: /// \ref amo93networkflows, \ref dasdan98minmeancycle.
kpeter@768: /// This class provides the most efficient algorithm for the
kpeter@768: /// minimum mean cycle problem, though the best known theoretical
kpeter@768: /// bound on its running time is exponential.
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: #ifdef DOXYGEN
kpeter@761: template <typename GR, typename LEN, typename TR>
kpeter@758: #else
kpeter@758: template < typename GR,
kpeter@761: typename LEN = typename GR::template ArcMap<int>,
kpeter@764: typename TR = HowardDefaultTraits<GR, LEN> >
kpeter@758: #endif
kpeter@764: class Howard
kpeter@758: {
kpeter@758: public:
kpeter@758:
kpeter@761: /// The type of the digraph
kpeter@761: typedef typename TR::Digraph Digraph;
kpeter@758: /// The type of the length map
kpeter@761: typedef typename TR::LengthMap LengthMap;
kpeter@758: /// The type of the arc lengths
kpeter@761: typedef typename TR::Value Value;
kpeter@761:
kpeter@761: /// \brief The large value type
kpeter@761: ///
kpeter@761: /// The large value type used for internal computations.
kpeter@764: /// Using the \ref HowardDefaultTraits "default traits class",
kpeter@761: /// it is \c long \c long if the \c Value type is integer,
kpeter@761: /// otherwise it is \c double.
kpeter@761: typedef typename TR::LargeValue LargeValue;
kpeter@761:
kpeter@761: /// The tolerance type
kpeter@761: typedef typename TR::Tolerance Tolerance;
kpeter@761:
kpeter@761: /// \brief The path type of the found cycles
kpeter@761: ///
kpeter@761: /// The path type of the found cycles.
kpeter@764: /// Using the \ref HowardDefaultTraits "default traits class",
kpeter@761: /// it is \ref lemon::Path "Path<Digraph>".
kpeter@761: typedef typename TR::Path Path;
kpeter@761:
kpeter@764: /// The \ref HowardDefaultTraits "traits class" of the algorithm
kpeter@761: typedef TR Traits;
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@760: // Data for the found cycles
kpeter@760: bool _curr_found, _best_found;
kpeter@761: LargeValue _curr_length, _best_length;
kpeter@760: int _curr_size, _best_size;
kpeter@760: Node _curr_node, _best_node;
kpeter@760:
kpeter@758: Path *_cycle_path;
kpeter@760: bool _local_path;
kpeter@758:
kpeter@760: // Internal data used by the algorithm
kpeter@760: typename Digraph::template NodeMap<Arc> _policy;
kpeter@760: typename Digraph::template NodeMap<bool> _reached;
kpeter@760: typename Digraph::template NodeMap<int> _level;
kpeter@761: typename Digraph::template NodeMap<LargeValue> _dist;
kpeter@758:
kpeter@760: // Data for storing the strongly connected components
kpeter@760: int _comp_num;
kpeter@758: typename Digraph::template NodeMap<int> _comp;
kpeter@760: std::vector<std::vector<Node> > _comp_nodes;
kpeter@760: std::vector<Node>* _nodes;
kpeter@760: typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
kpeter@760:
kpeter@760: // Queue used for BFS search
kpeter@760: std::vector<Node> _queue;
kpeter@760: int _qfront, _qback;
kpeter@761:
kpeter@761: Tolerance _tolerance;
kpeter@761:
kpeter@767: // Infinite constant
kpeter@767: const LargeValue INF;
kpeter@767:
kpeter@761: public:
kpeter@761:
kpeter@761: /// \name Named Template Parameters
kpeter@761: /// @{
kpeter@761:
kpeter@761: template <typename T>
kpeter@761: struct SetLargeValueTraits : public Traits {
kpeter@761: typedef T LargeValue;
kpeter@761: typedef lemon::Tolerance<T> Tolerance;
kpeter@761: };
kpeter@761:
kpeter@761: /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@761: /// \c LargeValue type.
kpeter@761: ///
kpeter@761: /// \ref named-templ-param "Named parameter" for setting \c LargeValue
kpeter@761: /// type. It is used for internal computations in the algorithm.
kpeter@761: template <typename T>
kpeter@761: struct SetLargeValue
kpeter@764: : public Howard<GR, LEN, SetLargeValueTraits<T> > {
kpeter@764: typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create;
kpeter@761: };
kpeter@761:
kpeter@761: template <typename T>
kpeter@761: struct SetPathTraits : public Traits {
kpeter@761: typedef T Path;
kpeter@761: };
kpeter@761:
kpeter@761: /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@761: /// \c %Path type.
kpeter@761: ///
kpeter@761: /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@761: /// type of the found cycles.
kpeter@761: /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@761: /// and it must have an \c addBack() function.
kpeter@761: template <typename T>
kpeter@761: struct SetPath
kpeter@764: : public Howard<GR, LEN, SetPathTraits<T> > {
kpeter@764: typedef Howard<GR, LEN, SetPathTraits<T> > Create;
kpeter@761: };
kpeter@760:
kpeter@761: /// @}
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@764: Howard( const Digraph &digraph,
kpeter@764: const LengthMap &length ) :
kpeter@767: _gr(digraph), _length(length), _best_found(false),
kpeter@767: _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false),
kpeter@760: _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
kpeter@767: _comp(digraph), _in_arcs(digraph),
kpeter@767: INF(std::numeric_limits<LargeValue>::has_infinity ?
kpeter@767: std::numeric_limits<LargeValue>::infinity() :
kpeter@767: std::numeric_limits<LargeValue>::max())
kpeter@758: {}
kpeter@758:
kpeter@758: /// Destructor.
kpeter@764: ~Howard() {
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@759: /// \ref findMinMean(), 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@764: Howard& cycle(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@769: /// \brief Set the tolerance used by the algorithm.
kpeter@769: ///
kpeter@769: /// This function sets the tolerance object used by the algorithm.
kpeter@769: ///
kpeter@769: /// \return <tt>(*this)</tt>
kpeter@769: Howard& tolerance(const Tolerance& tolerance) {
kpeter@769: _tolerance = tolerance;
kpeter@769: return *this;
kpeter@769: }
kpeter@769:
kpeter@769: /// \brief Return a const reference to the tolerance.
kpeter@769: ///
kpeter@769: /// This function returns a const reference to the tolerance object
kpeter@769: /// used by the algorithm.
kpeter@769: const Tolerance& tolerance() const {
kpeter@769: return _tolerance;
kpeter@769: }
kpeter@769:
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@759: /// If you only need the minimum mean length, you may call
kpeter@759: /// \ref findMinMean().
kpeter@758:
kpeter@758: /// @{
kpeter@758:
kpeter@758: /// \brief Run the algorithm.
kpeter@758: ///
kpeter@758: /// This function runs the algorithm.
kpeter@759: /// It can be called more than once (e.g. if the underlying digraph
kpeter@759: /// and/or the arc lengths have been modified).
kpeter@758: ///
kpeter@758: /// \return \c true if a directed cycle exists in the digraph.
kpeter@758: ///
kpeter@759: /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@758: /// \code
kpeter@759: /// return mmc.findMinMean() && mmc.findCycle();
kpeter@758: /// \endcode
kpeter@758: bool run() {
kpeter@758: return findMinMean() && findCycle();
kpeter@758: }
kpeter@758:
kpeter@759: /// \brief Find the minimum cycle mean.
kpeter@758: ///
kpeter@759: /// This function finds the minimum mean length of the directed
kpeter@759: /// cycles in the digraph.
kpeter@758: ///
kpeter@759: /// \return \c true if a directed cycle exists in the digraph.
kpeter@759: bool findMinMean() {
kpeter@760: // Initialize and find strongly connected components
kpeter@760: init();
kpeter@760: findComponents();
kpeter@760:
kpeter@759: // Find the minimum cycle mean in the components
kpeter@758: for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@760: // Find the minimum mean cycle in the current component
kpeter@760: if (!buildPolicyGraph(comp)) continue;
kpeter@758: while (true) {
kpeter@760: findPolicyCycle();
kpeter@758: if (!computeNodeDistances()) break;
kpeter@758: }
kpeter@760: // Update the best cycle (global minimum mean cycle)
kpeter@767: if ( _curr_found && (!_best_found ||
kpeter@760: _curr_length * _best_size < _best_length * _curr_size) ) {
kpeter@760: _best_found = true;
kpeter@760: _best_length = _curr_length;
kpeter@760: _best_size = _curr_size;
kpeter@760: _best_node = _curr_node;
kpeter@760: }
kpeter@758: }
kpeter@760: return _best_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@759: /// \pre \ref findMinMean() must be called before using this function.
kpeter@758: bool findCycle() {
kpeter@760: if (!_best_found) return false;
kpeter@760: _cycle_path->addBack(_policy[_best_node]);
kpeter@760: for ( Node v = _best_node;
kpeter@760: (v = _gr.target(_policy[v])) != _best_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@759: /// The results 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@760: /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758: /// using this function.
kpeter@761: LargeValue cycleLength() const {
kpeter@760: return _best_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@760: /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758: /// using this function.
kpeter@758: int cycleArcNum() const {
kpeter@760: return _best_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@760: /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@758: /// following code.
kpeter@758: /// \code
kpeter@760: /// return static_cast<double>(alg.cycleLength()) / alg.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@760: return static_cast<double>(_best_length) / _best_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: const Path& cycle() const {
kpeter@758: return *_cycle_path;
kpeter@758: }
kpeter@758:
kpeter@758: ///@}
kpeter@758:
kpeter@758: private:
kpeter@758:
kpeter@760: // Initialize
kpeter@760: void init() {
kpeter@760: if (!_cycle_path) {
kpeter@760: _local_path = true;
kpeter@760: _cycle_path = new Path;
kpeter@758: }
kpeter@760: _queue.resize(countNodes(_gr));
kpeter@760: _best_found = false;
kpeter@760: _best_length = 0;
kpeter@760: _best_size = 1;
kpeter@760: _cycle_path->clear();
kpeter@760: }
kpeter@760:
kpeter@760: // Find strongly connected components and initialize _comp_nodes
kpeter@760: // and _in_arcs
kpeter@760: void findComponents() {
kpeter@760: _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@760: _comp_nodes.resize(_comp_num);
kpeter@760: if (_comp_num == 1) {
kpeter@760: _comp_nodes[0].clear();
kpeter@760: for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760: _comp_nodes[0].push_back(n);
kpeter@760: _in_arcs[n].clear();
kpeter@760: for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760: _in_arcs[n].push_back(a);
kpeter@760: }
kpeter@760: }
kpeter@760: } else {
kpeter@760: for (int i = 0; i < _comp_num; ++i)
kpeter@760: _comp_nodes[i].clear();
kpeter@760: for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760: int k = _comp[n];
kpeter@760: _comp_nodes[k].push_back(n);
kpeter@760: _in_arcs[n].clear();
kpeter@760: for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760: if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
kpeter@760: }
kpeter@760: }
kpeter@758: }
kpeter@760: }
kpeter@760:
kpeter@760: // Build the policy graph in the given strongly connected component
kpeter@760: // (the out-degree of every node is 1)
kpeter@760: bool buildPolicyGraph(int comp) {
kpeter@760: _nodes = &(_comp_nodes[comp]);
kpeter@760: if (_nodes->size() < 1 ||
kpeter@760: (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@760: return false;
kpeter@758: }
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@767: _dist[(*_nodes)[i]] = INF;
kpeter@760: }
kpeter@760: Node u, v;
kpeter@760: Arc e;
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760: v = (*_nodes)[i];
kpeter@760: for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760: e = _in_arcs[v][j];
kpeter@760: u = _gr.source(e);
kpeter@760: if (_length[e] < _dist[u]) {
kpeter@760: _dist[u] = _length[e];
kpeter@760: _policy[u] = e;
kpeter@760: }
kpeter@758: }
kpeter@758: }
kpeter@758: return true;
kpeter@758: }
kpeter@758:
kpeter@760: // Find the minimum mean cycle in the policy graph
kpeter@760: void findPolicyCycle() {
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760: _level[(*_nodes)[i]] = -1;
kpeter@760: }
kpeter@761: LargeValue clength;
kpeter@758: int csize;
kpeter@758: Node u, v;
kpeter@760: _curr_found = false;
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760: u = (*_nodes)[i];
kpeter@760: if (_level[u] >= 0) continue;
kpeter@760: for (; _level[u] < 0; u = _gr.target(_policy[u])) {
kpeter@760: _level[u] = i;
kpeter@760: }
kpeter@760: if (_level[u] == i) {
kpeter@760: // A cycle is found
kpeter@760: clength = _length[_policy[u]];
kpeter@760: csize = 1;
kpeter@760: for (v = u; (v = _gr.target(_policy[v])) != u; ) {
kpeter@760: clength += _length[_policy[v]];
kpeter@760: ++csize;
kpeter@758: }
kpeter@760: if ( !_curr_found ||
kpeter@760: (clength * _curr_size < _curr_length * csize) ) {
kpeter@760: _curr_found = true;
kpeter@760: _curr_length = clength;
kpeter@760: _curr_size = csize;
kpeter@760: _curr_node = u;
kpeter@758: }
kpeter@758: }
kpeter@758: }
kpeter@758: }
kpeter@758:
kpeter@760: // Contract the policy graph and compute node distances
kpeter@758: bool computeNodeDistances() {
kpeter@760: // Find the component of the main cycle and compute node distances
kpeter@760: // using reverse BFS
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760: _reached[(*_nodes)[i]] = false;
kpeter@760: }
kpeter@760: _qfront = _qback = 0;
kpeter@760: _queue[0] = _curr_node;
kpeter@760: _reached[_curr_node] = true;
kpeter@760: _dist[_curr_node] = 0;
kpeter@758: Node u, v;
kpeter@760: Arc e;
kpeter@760: while (_qfront <= _qback) {
kpeter@760: v = _queue[_qfront++];
kpeter@760: for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760: e = _in_arcs[v][j];
kpeter@758: u = _gr.source(e);
kpeter@760: if (_policy[u] == e && !_reached[u]) {
kpeter@760: _reached[u] = true;
kpeter@761: _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@760: _queue[++_qback] = u;
kpeter@758: }
kpeter@758: }
kpeter@758: }
kpeter@760:
kpeter@760: // Connect all other nodes to this component and compute node
kpeter@760: // distances using reverse BFS
kpeter@760: _qfront = 0;
kpeter@760: while (_qback < int(_nodes->size())-1) {
kpeter@760: v = _queue[_qfront++];
kpeter@760: for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760: e = _in_arcs[v][j];
kpeter@760: u = _gr.source(e);
kpeter@760: if (!_reached[u]) {
kpeter@760: _reached[u] = true;
kpeter@760: _policy[u] = e;
kpeter@761: _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@760: _queue[++_qback] = u;
kpeter@760: }
kpeter@760: }
kpeter@760: }
kpeter@760:
kpeter@760: // Improve node distances
kpeter@758: bool improved = false;
kpeter@760: for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760: v = (*_nodes)[i];
kpeter@760: for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760: e = _in_arcs[v][j];
kpeter@760: u = _gr.source(e);
kpeter@761: LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@761: if (_tolerance.less(delta, _dist[u])) {
kpeter@760: _dist[u] = delta;
kpeter@760: _policy[u] = e;
kpeter@760: improved = true;
kpeter@760: }
kpeter@758: }
kpeter@758: }
kpeter@758: return improved;
kpeter@758: }
kpeter@758:
kpeter@764: }; //class Howard
kpeter@758:
kpeter@758: ///@}
kpeter@758:
kpeter@758: } //namespace lemon
kpeter@758:
kpeter@764: #endif //LEMON_HOWARD_H