/* -*- 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_SUURBALLE_H #define LEMON_SUURBALLE_H ///\ingroup shortest_path ///\file ///\brief An algorithm for finding arc-disjoint paths between two /// nodes having minimum total length. #include #include #include namespace lemon { /// \addtogroup shortest_path /// @{ /// \brief Algorithm for finding arc-disjoint paths between two nodes /// having minimum total length. /// /// \ref lemon::Suurballe "Suurballe" implements an algorithm for /// finding arc-disjoint paths having minimum total length (cost) /// from a given source node to a given target node in a digraph. /// /// In fact, this implementation is the specialization of the /// \ref CapacityScaling "successive shortest path" algorithm. /// /// \tparam Digraph The digraph type the algorithm runs on. /// The default value is \c ListDigraph. /// \tparam LengthMap The type of the length (cost) map. /// The default value is Digraph::ArcMap. /// /// \warning Length values should be \e non-negative \e integers. /// /// \note For finding node-disjoint paths this algorithm can be used /// with \ref SplitNodes. #ifdef DOXYGEN template #else template < typename Digraph = ListDigraph, typename LengthMap = typename Digraph::template ArcMap > #endif class Suurballe { TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); typedef typename LengthMap::Value Length; typedef ConstMap ConstArcMap; typedef typename Digraph::template NodeMap PredMap; public: /// The type of the flow map. typedef typename Digraph::template ArcMap FlowMap; /// The type of the potential map. typedef typename Digraph::template NodeMap PotentialMap; /// The type of the path structures. typedef SimplePath Path; private: /// \brief Special implementation of the Dijkstra algorithm /// for finding shortest paths in the residual network. /// /// \ref ResidualDijkstra is a special implementation of the /// \ref Dijkstra algorithm for finding shortest paths in the /// residual network of the digraph with respect to the reduced arc /// lengths and modifying the node potentials according to the /// distance of the nodes. class ResidualDijkstra { typedef typename Digraph::template NodeMap HeapCrossRef; typedef BinHeap Heap; private: // The digraph the algorithm runs on const Digraph &_graph; // The main maps const FlowMap &_flow; const LengthMap &_length; PotentialMap &_potential; // The distance map PotentialMap _dist; // The pred arc map PredMap &_pred; // The processed (i.e. permanently labeled) nodes std::vector _proc_nodes; Node _s; Node _t; public: /// Constructor. ResidualDijkstra( const Digraph &digraph, const FlowMap &flow, const LengthMap &length, PotentialMap &potential, PredMap &pred, Node s, Node t ) : _graph(digraph), _flow(flow), _length(length), _potential(potential), _dist(digraph), _pred(pred), _s(s), _t(t) {} /// \brief Run the algorithm. It returns \c true if a path is found /// from the source node to the target node. bool run() { HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); Heap heap(heap_cross_ref); heap.push(_s, 0); _pred[_s] = INVALID; _proc_nodes.clear(); // Process nodes while (!heap.empty() && heap.top() != _t) { Node u = heap.top(), v; Length d = heap.prio() + _potential[u], nd; _dist[u] = heap.prio(); heap.pop(); _proc_nodes.push_back(u); // Traverse outgoing arcs for (OutArcIt e(_graph, u); e != INVALID; ++e) { if (_flow[e] == 0) { v = _graph.target(e); switch(heap.state(v)) { case Heap::PRE_HEAP: heap.push(v, d + _length[e] - _potential[v]); _pred[v] = e; break; case Heap::IN_HEAP: nd = d + _length[e] - _potential[v]; if (nd < heap[v]) { heap.decrease(v, nd); _pred[v] = e; } break; case Heap::POST_HEAP: break; } } } // Traverse incoming arcs for (InArcIt e(_graph, u); e != INVALID; ++e) { if (_flow[e] == 1) { v = _graph.source(e); switch(heap.state(v)) { case Heap::PRE_HEAP: heap.push(v, d - _length[e] - _potential[v]); _pred[v] = e; break; case Heap::IN_HEAP: nd = d - _length[e] - _potential[v]; if (nd < heap[v]) { heap.decrease(v, nd); _pred[v] = e; } break; case Heap::POST_HEAP: break; } } } } if (heap.empty()) return false; // Update potentials of processed nodes Length t_dist = heap.prio(); for (int i = 0; i < int(_proc_nodes.size()); ++i) _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; return true; } }; //class ResidualDijkstra private: // The digraph the algorithm runs on const Digraph &_graph; // The length map const LengthMap &_length; // Arc map of the current flow FlowMap *_flow; bool _local_flow; // Node map of the current potentials PotentialMap *_potential; bool _local_potential; // The source node Node _source; // The target node Node _target; // Container to store the found paths std::vector< SimplePath > paths; int _path_num; // The pred arc map PredMap _pred; // Implementation of the Dijkstra algorithm for finding augmenting // shortest paths in the residual network ResidualDijkstra *_dijkstra; public: /// \brief Constructor. /// /// Constructor. /// /// \param digraph The digraph the algorithm runs on. /// \param length The length (cost) values of the arcs. /// \param s The source node. /// \param t The target node. Suurballe( const Digraph &digraph, const LengthMap &length, Node s, Node t ) : _graph(digraph), _length(length), _flow(0), _local_flow(false), _potential(0), _local_potential(false), _source(s), _target(t), _pred(digraph) {} /// Destructor. ~Suurballe() { if (_local_flow) delete _flow; if (_local_potential) delete _potential; delete _dijkstra; } /// \brief Set the flow map. /// /// This function sets the flow map. /// /// The found flow contains only 0 and 1 values. It is the union of /// the found arc-disjoint paths. /// /// \return \c (*this) Suurballe& flowMap(FlowMap &map) { if (_local_flow) { delete _flow; _local_flow = false; } _flow = ↦ return *this; } /// \brief Set the potential map. /// /// This function sets the potential map. /// /// The potentials provide the dual solution of the underlying /// minimum cost flow problem. /// /// \return \c (*this) Suurballe& potentialMap(PotentialMap &map) { if (_local_potential) { delete _potential; _local_potential = false; } _potential = ↦ return *this; } /// \name Execution control /// The simplest way to execute the algorithm is to call the run() /// function. /// \n /// If you only need the flow that is the union of the found /// arc-disjoint paths, you may call init() and findFlow(). /// @{ /// \brief Run the algorithm. /// /// This function runs the algorithm. /// /// \param k The number of paths to be found. /// /// \return \c k if there are at least \c k arc-disjoint paths from /// \c s to \c t in the digraph. Otherwise it returns the number of /// arc-disjoint paths found. /// /// \note Apart from the return value, s.run(k) is just a /// shortcut of the following code. /// \code /// s.init(); /// s.findFlow(k); /// s.findPaths(); /// \endcode int run(int k = 2) { init(); findFlow(k); findPaths(); return _path_num; } /// \brief Initialize the algorithm. /// /// This function initializes the algorithm. void init() { // Initialize maps if (!_flow) { _flow = new FlowMap(_graph); _local_flow = true; } if (!_potential) { _potential = new PotentialMap(_graph); _local_potential = true; } for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; _dijkstra = new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred, _source, _target ); } /// \brief Execute the successive shortest path algorithm to find /// an optimal flow. /// /// This function executes the successive shortest path algorithm to /// find a minimum cost flow, which is the union of \c k or less /// arc-disjoint paths. /// /// \return \c k if there are at least \c k arc-disjoint paths from /// \c s to \c t in the digraph. Otherwise it returns the number of /// arc-disjoint paths found. /// /// \pre \ref init() must be called before using this function. int findFlow(int k = 2) { // Find shortest paths _path_num = 0; while (_path_num < k) { // Run Dijkstra if (!_dijkstra->run()) break; ++_path_num; // Set the flow along the found shortest path Node u = _target; Arc e; while ((e = _pred[u]) != INVALID) { if (u == _graph.target(e)) { (*_flow)[e] = 1; u = _graph.source(e); } else { (*_flow)[e] = 0; u = _graph.target(e); } } } return _path_num; } /// \brief Compute the paths from the flow. /// /// This function computes the paths from the flow. /// /// \pre \ref init() and \ref findFlow() must be called before using /// this function. void findPaths() { // Create the residual flow map (the union of the paths not found // so far) FlowMap res_flow(_graph); for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; paths.clear(); paths.resize(_path_num); for (int i = 0; i < _path_num; ++i) { Node n = _source; while (n != _target) { OutArcIt e(_graph, n); for ( ; res_flow[e] == 0; ++e) ; n = _graph.target(e); paths[i].addBack(e); res_flow[e] = 0; } } } /// @} /// \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 a const reference to the arc map storing the /// found flow. /// /// This function returns a const reference to the arc map storing /// the flow that is the union of the found arc-disjoint paths. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. const FlowMap& flowMap() const { return *_flow; } /// \brief Return a const reference to the node map storing the /// found potentials (the dual solution). /// /// This function returns a const reference to the node map storing /// the found potentials that provide the dual solution of the /// underlying minimum cost flow problem. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. const PotentialMap& potentialMap() const { return *_potential; } /// \brief Return the flow on the given arc. /// /// This function returns the flow on the given arc. /// It is \c 1 if the arc is involved in one of the found paths, /// otherwise it is \c 0. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. int flow(const Arc& arc) const { return (*_flow)[arc]; } /// \brief Return the potential of the given node. /// /// This function returns the potential of the given node. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. Length potential(const Node& node) const { return (*_potential)[node]; } /// \brief Return the total length (cost) of the found paths (flow). /// /// This function returns the total length (cost) of the found paths /// (flow). The complexity of the function is \f$O(e) \f$. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. Length totalLength() const { Length c = 0; for (ArcIt e(_graph); e != INVALID; ++e) c += (*_flow)[e] * _length[e]; return c; } /// \brief Return the number of the found paths. /// /// This function returns the number of the found paths. /// /// \pre \ref run() or \ref findFlow() must be called before using /// this function. int pathNum() const { return _path_num; } /// \brief Return a const reference to the specified path. /// /// This function returns a const reference to the specified path. /// /// \param i The function returns the \c i-th path. /// \c i must be between \c 0 and %pathNum()-1. /// /// \pre \ref run() or \ref findPaths() must be called before using /// this function. Path path(int i) const { return paths[i]; } /// @} }; //class Suurballe ///@} } //namespace lemon #endif //LEMON_SUURBALLE_H