alpar@906: /* -*- C++ -*-
alpar@906:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@906:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
alpar@906:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
alpar@906:  *
alpar@906:  */
alpar@906: 
alpar@921: #ifndef LEMON_SUURBALLE_H
alpar@921: #define LEMON_SUURBALLE_H
alpar@899: 
deba@2378: ///\ingroup shortest_path
alpar@899: ///\file
kpeter@2586: ///\brief An algorithm for finding edge-disjoint paths between two
kpeter@2586: /// nodes having minimum total length.
alpar@899: 
alpar@899: #include <vector>
kpeter@2586: #include <lemon/bin_heap.h>
deba@2335: #include <lemon/path.h>
alpar@899: 
alpar@921: namespace lemon {
alpar@899: 
kpeter@2586:   /// \addtogroup shortest_path
kpeter@2586:   /// @{
alpar@899: 
kpeter@2586:   /// \brief Implementation of an algorithm for finding edge-disjoint
kpeter@2586:   /// paths between two nodes having minimum total length.
alpar@899:   ///
kpeter@2586:   /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
kpeter@2586:   /// finding edge-disjoint paths having minimum total length (cost)
kpeter@2586:   /// from a given source node to a given target node in a directed
kpeter@2586:   /// graph.
alpar@899:   ///
kpeter@2586:   /// In fact, this implementation is the specialization of the
kpeter@2586:   /// \ref CapacityScaling "successive shortest path" algorithm.
alpar@899:   ///
kpeter@2586:   /// \tparam Graph The directed graph type the algorithm runs on.
kpeter@2586:   /// \tparam LengthMap The type of the length (cost) map.
kpeter@2586:   ///
kpeter@2586:   /// \warning Length values should be \e non-negative \e integers.
kpeter@2586:   ///
kpeter@2586:   /// \note For finding node-disjoint paths this algorithm can be used
kpeter@2586:   /// with \ref SplitGraphAdaptor.
kpeter@2586:   ///
kpeter@2586:   /// \author Attila Bernath and Peter Kovacs
kpeter@2586:   
kpeter@2586:   template < typename Graph, 
kpeter@2586:              typename LengthMap = typename Graph::template EdgeMap<int> >
kpeter@2586:   class Suurballe
kpeter@2586:   {
kpeter@2586:     GRAPH_TYPEDEFS(typename Graph);
alpar@899: 
alpar@987:     typedef typename LengthMap::Value Length;
kpeter@2586:     typedef ConstMap<Edge, int> ConstEdgeMap;
kpeter@2586:     typedef typename Graph::template NodeMap<Edge> PredMap;
kpeter@2586: 
kpeter@2586:   public:
kpeter@2586: 
kpeter@2586:     /// The type of the flow map.
kpeter@2586:     typedef typename Graph::template EdgeMap<int> FlowMap;
kpeter@2586:     /// The type of the potential map.
kpeter@2586:     typedef typename Graph::template NodeMap<Length> PotentialMap;
kpeter@2586:     /// The type of the path structures.
kpeter@2586:     typedef SimplePath<Graph> Path;
kpeter@2586: 
kpeter@2586:   private:
kpeter@2586:   
kpeter@2586:     /// \brief Special implementation of the \ref Dijkstra algorithm
kpeter@2586:     /// for finding shortest paths in the residual network.
kpeter@2586:     ///
kpeter@2586:     /// \ref ResidualDijkstra is a special implementation of the
kpeter@2586:     /// \ref Dijkstra algorithm for finding shortest paths in the
kpeter@2586:     /// residual network of the graph with respect to the reduced edge
kpeter@2586:     /// lengths and modifying the node potentials according to the
kpeter@2586:     /// distance of the nodes.
kpeter@2586:     class ResidualDijkstra
kpeter@2586:     {
kpeter@2586:       typedef typename Graph::template NodeMap<int> HeapCrossRef;
kpeter@2586:       typedef BinHeap<Length, HeapCrossRef> Heap;
kpeter@2586: 
kpeter@2586:     private:
kpeter@2586: 
kpeter@2586:       // The directed graph the algorithm runs on
kpeter@2586:       const Graph &_graph;
kpeter@2586: 
kpeter@2586:       // The main maps
kpeter@2586:       const FlowMap &_flow;
kpeter@2586:       const LengthMap &_length;
kpeter@2586:       PotentialMap &_potential;
kpeter@2586: 
kpeter@2586:       // The distance map
kpeter@2586:       PotentialMap _dist;
kpeter@2586:       // The pred edge map
kpeter@2586:       PredMap &_pred;
kpeter@2586:       // The processed (i.e. permanently labeled) nodes
kpeter@2586:       std::vector<Node> _proc_nodes;
kpeter@2586:       
kpeter@2586:       Node _s;
kpeter@2586:       Node _t;
kpeter@2586: 
kpeter@2586:     public:
kpeter@2586: 
kpeter@2586:       /// Constructor.
kpeter@2586:       ResidualDijkstra( const Graph &graph,
kpeter@2586:                         const FlowMap &flow,
kpeter@2586:                         const LengthMap &length,
kpeter@2586:                         PotentialMap &potential,
kpeter@2586:                         PredMap &pred,
kpeter@2586:                         Node s, Node t ) :
kpeter@2586:         _graph(graph), _flow(flow), _length(length), _potential(potential),
kpeter@2586:         _dist(graph), _pred(pred), _s(s), _t(t) {}
kpeter@2586: 
kpeter@2586:       /// \brief Runs the algorithm. Returns \c true if a path is found
kpeter@2586:       /// from the source node to the target node.
kpeter@2586:       bool run() {
kpeter@2586:         HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
kpeter@2586:         Heap heap(heap_cross_ref);
kpeter@2586:         heap.push(_s, 0);
kpeter@2586:         _pred[_s] = INVALID;
kpeter@2586:         _proc_nodes.clear();
kpeter@2586: 
kpeter@2586:         // Processing nodes
kpeter@2586:         while (!heap.empty() && heap.top() != _t) {
kpeter@2586:           Node u = heap.top(), v;
kpeter@2586:           Length d = heap.prio() + _potential[u], nd;
kpeter@2586:           _dist[u] = heap.prio();
kpeter@2586:           heap.pop();
kpeter@2586:           _proc_nodes.push_back(u);
kpeter@2586: 
kpeter@2586:           // Traversing outgoing edges
kpeter@2586:           for (OutEdgeIt e(_graph, u); e != INVALID; ++e) {
kpeter@2586:             if (_flow[e] == 0) {
kpeter@2586:               v = _graph.target(e);
kpeter@2586:               switch(heap.state(v)) {
kpeter@2586:               case Heap::PRE_HEAP:
kpeter@2586:                 heap.push(v, d + _length[e] - _potential[v]);
kpeter@2586:                 _pred[v] = e;
kpeter@2586:                 break;
kpeter@2586:               case Heap::IN_HEAP:
kpeter@2586:                 nd = d + _length[e] - _potential[v];
kpeter@2586:                 if (nd < heap[v]) {
kpeter@2586:                   heap.decrease(v, nd);
kpeter@2586:                   _pred[v] = e;
kpeter@2586:                 }
kpeter@2586:                 break;
kpeter@2586:               case Heap::POST_HEAP:
kpeter@2586:                 break;
kpeter@2586:               }
kpeter@2586:             }
kpeter@2586:           }
kpeter@2586: 
kpeter@2586:           // Traversing incoming edges
kpeter@2586:           for (InEdgeIt e(_graph, u); e != INVALID; ++e) {
kpeter@2586:             if (_flow[e] == 1) {
kpeter@2586:               v = _graph.source(e);
kpeter@2586:               switch(heap.state(v)) {
kpeter@2586:               case Heap::PRE_HEAP:
kpeter@2586:                 heap.push(v, d - _length[e] - _potential[v]);
kpeter@2586:                 _pred[v] = e;
kpeter@2586:                 break;
kpeter@2586:               case Heap::IN_HEAP:
kpeter@2586:                 nd = d - _length[e] - _potential[v];
kpeter@2586:                 if (nd < heap[v]) {
kpeter@2586:                   heap.decrease(v, nd);
kpeter@2586:                   _pred[v] = e;
kpeter@2586:                 }
kpeter@2586:                 break;
kpeter@2586:               case Heap::POST_HEAP:
kpeter@2586:                 break;
kpeter@2586:               }
kpeter@2586:             }
kpeter@2586:           }
kpeter@2586:         }
kpeter@2586:         if (heap.empty()) return false;
kpeter@2586: 
kpeter@2586:         // Updating potentials of processed nodes
kpeter@2586:         Length t_dist = heap.prio();
kpeter@2586:         for (int i = 0; i < int(_proc_nodes.size()); ++i)
kpeter@2586:           _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
kpeter@2586:         return true;
kpeter@2586:       }
kpeter@2586: 
kpeter@2586:     }; //class ResidualDijkstra
kpeter@2586: 
kpeter@2586:   private:
kpeter@2586: 
kpeter@2586:     // The directed graph the algorithm runs on
kpeter@2586:     const Graph &_graph;
kpeter@2586:     // The length map
kpeter@2586:     const LengthMap &_length;
alpar@899:     
kpeter@2586:     // Edge map of the current flow
kpeter@2586:     FlowMap *_flow;
kpeter@2586:     bool _local_flow;
kpeter@2586:     // Node map of the current potentials
kpeter@2586:     PotentialMap *_potential;
kpeter@2586:     bool _local_potential;
alpar@899: 
kpeter@2586:     // The source node
kpeter@2586:     Node _source;
kpeter@2586:     // The target node
kpeter@2586:     Node _target;
alpar@899: 
kpeter@2586:     // Container to store the found paths
kpeter@2586:     std::vector< SimplePath<Graph> > paths;
kpeter@2586:     int _path_num;
alpar@899: 
kpeter@2586:     // The pred edge map
kpeter@2586:     PredMap _pred;
kpeter@2586:     // Implementation of the Dijkstra algorithm for finding augmenting
kpeter@2586:     // shortest paths in the residual network
kpeter@2586:     ResidualDijkstra *_dijkstra;
marci@941: 
kpeter@2586:   public:
alpar@899: 
kpeter@2586:     /// \brief Constructor.
kpeter@2586:     ///
kpeter@2586:     /// Constructor.
kpeter@2586:     ///
kpeter@2586:     /// \param graph The directed graph the algorithm runs on.
kpeter@2586:     /// \param length The length (cost) values of the edges.
kpeter@2586:     /// \param s The source node.
kpeter@2586:     /// \param t The target node.
kpeter@2586:     Suurballe( const Graph &graph,
kpeter@2586:                const LengthMap &length,
kpeter@2586:                Node s, Node t ) :
kpeter@2586:       _graph(graph), _length(length), _flow(0), _local_flow(false),
kpeter@2586:       _potential(0), _local_potential(false), _source(s), _target(t),
kpeter@2586:       _pred(graph) {}
alpar@899: 
kpeter@2586:     /// Destructor.
kpeter@2586:     ~Suurballe() {
kpeter@2586:       if (_local_flow) delete _flow;
kpeter@2586:       if (_local_potential) delete _potential;
kpeter@2586:       delete _dijkstra;
kpeter@2586:     }
alpar@899: 
kpeter@2586:     /// \brief Sets the flow map.
kpeter@2586:     ///
kpeter@2586:     /// Sets the flow map.
kpeter@2586:     ///
kpeter@2586:     /// The found flow contains only 0 and 1 values. It is the union of
kpeter@2586:     /// the found edge-disjoint paths.
kpeter@2586:     ///
kpeter@2586:     /// \return \c (*this)
kpeter@2586:     Suurballe& flowMap(FlowMap &map) {
kpeter@2586:       if (_local_flow) {
kpeter@2586:         delete _flow;
kpeter@2586:         _local_flow = false;
kpeter@2586:       }
kpeter@2586:       _flow = &map;
kpeter@2586:       return *this;
kpeter@2586:     }
alpar@899: 
kpeter@2586:     /// \brief Sets the potential map.
deba@2276:     ///
kpeter@2586:     /// Sets the potential map.
kpeter@2586:     ///
kpeter@2586:     /// The potentials provide the dual solution of the underlying 
kpeter@2586:     /// minimum cost flow problem.
kpeter@2586:     ///
kpeter@2586:     /// \return \c (*this)
kpeter@2586:     Suurballe& potentialMap(PotentialMap &map) {
kpeter@2586:       if (_local_potential) {
kpeter@2586:         delete _potential;
kpeter@2586:         _local_potential = false;
kpeter@2586:       }
kpeter@2586:       _potential = &map;
kpeter@2586:       return *this;
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// \name Execution control
kpeter@2586:     /// The simplest way to execute the algorithm is to call the run()
kpeter@2586:     /// function.
kpeter@2586:     /// \n
kpeter@2586:     /// If you only need the flow that is the union of the found
kpeter@2586:     /// edge-disjoint paths, you may call init() and findFlow().
kpeter@2586: 
kpeter@2586:     /// @{
alpar@899: 
deba@2276:     /// \brief Runs the algorithm.
alpar@899:     ///
deba@2276:     /// Runs the algorithm.
deba@2276:     ///
kpeter@2586:     /// \param k The number of paths to be found.
alpar@899:     ///
kpeter@2586:     /// \return \c k if there are at least \c k edge-disjoint paths
kpeter@2586:     /// from \c s to \c t. Otherwise it returns the number of
kpeter@2586:     /// edge-disjoint paths found.
kpeter@2586:     ///
kpeter@2586:     /// \note Apart from the return value, <tt>s.run(k)</tt> is just a
kpeter@2586:     /// shortcut of the following code.
kpeter@2586:     /// \code
kpeter@2586:     ///   s.init();
kpeter@2586:     ///   s.findFlow(k);
kpeter@2586:     ///   s.findPaths();
kpeter@2586:     /// \endcode
kpeter@2586:     int run(int k = 2) {
kpeter@2586:       init();
kpeter@2586:       findFlow(k);
kpeter@2586:       findPaths();
kpeter@2586:       return _path_num;
alpar@899:     }
alpar@899: 
kpeter@2586:     /// \brief Initializes the algorithm.
deba@2276:     ///
kpeter@2586:     /// Initializes the algorithm.
kpeter@2586:     void init() {
kpeter@2586:       // Initializing maps
kpeter@2586:       if (!_flow) {
kpeter@2586:         _flow = new FlowMap(_graph);
kpeter@2586:         _local_flow = true;
kpeter@2586:       }
kpeter@2586:       if (!_potential) {
kpeter@2586:         _potential = new PotentialMap(_graph);
kpeter@2586:         _local_potential = true;
kpeter@2586:       }
kpeter@2586:       for (EdgeIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
kpeter@2586:       for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
kpeter@2586: 
kpeter@2586:       _dijkstra = new ResidualDijkstra( _graph, *_flow, _length, 
kpeter@2586:                                         *_potential, _pred,
kpeter@2586:                                         _source, _target );
alpar@899:     }
alpar@899: 
kpeter@2586:     /// \brief Executes the successive shortest path algorithm to find
kpeter@2586:     /// an optimal flow.
deba@2276:     ///
kpeter@2586:     /// Executes the successive shortest path algorithm to find a
kpeter@2586:     /// minimum cost flow, which is the union of \c k or less
kpeter@2586:     /// edge-disjoint paths.
kpeter@2586:     ///
kpeter@2586:     /// \return \c k if there are at least \c k edge-disjoint paths
kpeter@2586:     /// from \c s to \c t. Otherwise it returns the number of
kpeter@2586:     /// edge-disjoint paths found.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref init() must be called before using this function.
kpeter@2586:     int findFlow(int k = 2) {
kpeter@2586:       // Finding shortest paths
kpeter@2586:       _path_num = 0;
kpeter@2586:       while (_path_num < k) {
kpeter@2586:         // Running Dijkstra
kpeter@2586:         if (!_dijkstra->run()) break;
kpeter@2586:         ++_path_num;
alpar@899: 
kpeter@2586:         // Setting the flow along the found shortest path
kpeter@2586:         Node u = _target;
kpeter@2586:         Edge e;
kpeter@2586:         while ((e = _pred[u]) != INVALID) {
kpeter@2586:           if (u == _graph.target(e)) {
kpeter@2586:             (*_flow)[e] = 1;
kpeter@2586:             u = _graph.source(e);
kpeter@2586:           } else {
kpeter@2586:             (*_flow)[e] = 0;
kpeter@2586:             u = _graph.target(e);
kpeter@2586:           }
kpeter@2586:         }
kpeter@2586:       }
kpeter@2586:       return _path_num;
kpeter@2586:     }
kpeter@2586:     
kpeter@2586:     /// \brief Computes the paths from the flow.
deba@2276:     ///
kpeter@2586:     /// Computes the paths from the flow.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref init() and \ref findFlow() must be called before using
kpeter@2586:     /// this function.
kpeter@2586:     void findPaths() {
kpeter@2586:       // Creating the residual flow map (the union of the paths not
kpeter@2586:       // found so far)
kpeter@2586:       FlowMap res_flow(*_flow);
alpar@899: 
kpeter@2586:       paths.clear();
kpeter@2586:       paths.resize(_path_num);
kpeter@2586:       for (int i = 0; i < _path_num; ++i) {
kpeter@2586:         Node n = _source;
kpeter@2586:         while (n != _target) {
kpeter@2586:           OutEdgeIt e(_graph, n);
kpeter@2586:           for ( ; res_flow[e] == 0; ++e) ;
kpeter@2586:           n = _graph.target(e);
kpeter@2586:           paths[i].addBack(e);
kpeter@2586:           res_flow[e] = 0;
kpeter@2586:         }
kpeter@2586:       }
alpar@899:     }
alpar@899: 
kpeter@2586:     /// @}
deba@2335: 
kpeter@2586:     /// \name Query Functions
kpeter@2586:     /// The result of the algorithm can be obtained using these
kpeter@2586:     /// functions.
kpeter@2586:     /// \n The algorithm should be executed before using them.
kpeter@2586: 
kpeter@2586:     /// @{
kpeter@2586: 
kpeter@2586:     /// \brief Returns a const reference to the edge map storing the
kpeter@2586:     /// found flow.
alpar@899:     ///
kpeter@2586:     /// Returns a const reference to the edge map storing the flow that
kpeter@2586:     /// is the union of the found edge-disjoint paths.
deba@2276:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     const FlowMap& flowMap() const {
kpeter@2586:       return *_flow;
deba@2335:     }
alpar@899: 
kpeter@2586:     /// \brief Returns a const reference to the node map storing the
kpeter@2586:     /// found potentials (the dual solution).
deba@2335:     ///
kpeter@2586:     /// Returns a const reference to the node map storing the found
kpeter@2586:     /// potentials that provide the dual solution of the underlying 
kpeter@2586:     /// minimum cost flow problem.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     const PotentialMap& potentialMap() const {
kpeter@2586:       return *_potential;
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// \brief Returns the flow on the given edge.
kpeter@2586:     ///
kpeter@2586:     /// Returns the flow on the given edge.
kpeter@2586:     /// It is \c 1 if the edge is involved in one of the found paths,
kpeter@2586:     /// otherwise it is \c 0.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     int flow(const Edge& edge) const {
kpeter@2586:       return (*_flow)[edge];
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// \brief Returns the potential of the given node.
kpeter@2586:     ///
kpeter@2586:     /// Returns the potential of the given node.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     Length potential(const Node& node) const {
kpeter@2586:       return (*_potential)[node];
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// \brief Returns the total length (cost) of the found paths (flow).
kpeter@2586:     ///
kpeter@2586:     /// Returns the total length (cost) of the found paths (flow).
kpeter@2586:     /// The complexity of the function is \f$ O(e) \f$.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     Length totalLength() const {
kpeter@2586:       Length c = 0;
kpeter@2586:       for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2586:         c += (*_flow)[e] * _length[e];
kpeter@2586:       return c;
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// \brief Returns the number of the found paths.
kpeter@2586:     ///
kpeter@2586:     /// Returns the number of the found paths.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findFlow() must be called before using this
kpeter@2586:     /// function.
deba@2335:     int pathNum() const {
kpeter@2586:       return _path_num;
alpar@899:     }
alpar@899: 
kpeter@2586:     /// \brief Returns a const reference to the specified path.
kpeter@2586:     ///
kpeter@2586:     /// Returns a const reference to the specified path.
kpeter@2586:     ///
kpeter@2586:     /// \param i The function returns the \c i-th path.
kpeter@2586:     /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
kpeter@2586:     ///
kpeter@2586:     /// \pre \ref run() or findPaths() must be called before using this
kpeter@2586:     /// function.
kpeter@2586:     Path path(int i) const {
kpeter@2586:       return paths[i];
kpeter@2586:     }
kpeter@2586: 
kpeter@2586:     /// @}
kpeter@2586: 
alpar@899:   }; //class Suurballe
alpar@899: 
alpar@899:   ///@}
alpar@899: 
alpar@921: } //namespace lemon
alpar@899: 
alpar@921: #endif //LEMON_SUURBALLE_H