lemon/suurballe.h
changeset 993 ad40f7d32846
parent 863 a93f1a27d831
     1.1 --- a/lemon/suurballe.h	Fri Aug 09 11:07:27 2013 +0200
     1.2 +++ b/lemon/suurballe.h	Sun Aug 11 15:28:12 2013 +0200
     1.3 @@ -2,7 +2,7 @@
     1.4   *
     1.5   * This file is a part of LEMON, a generic C++ optimization library.
     1.6   *
     1.7 - * Copyright (C) 2003-2009
     1.8 + * Copyright (C) 2003-2010
     1.9   * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10   * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11   *
    1.12 @@ -29,10 +29,54 @@
    1.13  #include <lemon/bin_heap.h>
    1.14  #include <lemon/path.h>
    1.15  #include <lemon/list_graph.h>
    1.16 +#include <lemon/dijkstra.h>
    1.17  #include <lemon/maps.h>
    1.18  
    1.19  namespace lemon {
    1.20  
    1.21 +  /// \brief Default traits class of Suurballe algorithm.
    1.22 +  ///
    1.23 +  /// Default traits class of Suurballe algorithm.
    1.24 +  /// \tparam GR The digraph type the algorithm runs on.
    1.25 +  /// \tparam LEN The type of the length map.
    1.26 +  /// The default value is <tt>GR::ArcMap<int></tt>.
    1.27 +#ifdef DOXYGEN
    1.28 +  template <typename GR, typename LEN>
    1.29 +#else
    1.30 +  template < typename GR,
    1.31 +             typename LEN = typename GR::template ArcMap<int> >
    1.32 +#endif
    1.33 +  struct SuurballeDefaultTraits
    1.34 +  {
    1.35 +    /// The type of the digraph.
    1.36 +    typedef GR Digraph;
    1.37 +    /// The type of the length map.
    1.38 +    typedef LEN LengthMap;
    1.39 +    /// The type of the lengths.
    1.40 +    typedef typename LEN::Value Length;
    1.41 +    /// The type of the flow map.
    1.42 +    typedef typename GR::template ArcMap<int> FlowMap;
    1.43 +    /// The type of the potential map.
    1.44 +    typedef typename GR::template NodeMap<Length> PotentialMap;
    1.45 +
    1.46 +    /// \brief The path type
    1.47 +    ///
    1.48 +    /// The type used for storing the found arc-disjoint paths.
    1.49 +    /// It must conform to the \ref lemon::concepts::Path "Path" concept
    1.50 +    /// and it must have an \c addBack() function.
    1.51 +    typedef lemon::Path<Digraph> Path;
    1.52 +
    1.53 +    /// The cross reference type used for the heap.
    1.54 +    typedef typename GR::template NodeMap<int> HeapCrossRef;
    1.55 +
    1.56 +    /// \brief The heap type used for internal Dijkstra computations.
    1.57 +    ///
    1.58 +    /// The type of the heap used for internal Dijkstra computations.
    1.59 +    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept
    1.60 +    /// and its priority type must be \c Length.
    1.61 +    typedef BinHeap<Length, HeapCrossRef> Heap;
    1.62 +  };
    1.63 +
    1.64    /// \addtogroup shortest_path
    1.65    /// @{
    1.66  
    1.67 @@ -46,7 +90,7 @@
    1.68    /// Note that this problem is a special case of the \ref min_cost_flow
    1.69    /// "minimum cost flow problem". This implementation is actually an
    1.70    /// efficient specialized version of the \ref CapacityScaling
    1.71 -  /// "Successive Shortest Path" algorithm directly for this problem.
    1.72 +  /// "successive shortest path" algorithm directly for this problem.
    1.73    /// Therefore this class provides query functions for flow values and
    1.74    /// node potentials (the dual solution) just like the minimum cost flow
    1.75    /// algorithms.
    1.76 @@ -57,13 +101,14 @@
    1.77    ///
    1.78    /// \warning Length values should be \e non-negative.
    1.79    ///
    1.80 -  /// \note For finding node-disjoint paths this algorithm can be used
    1.81 +  /// \note For finding \e node-disjoint paths, this algorithm can be used
    1.82    /// along with the \ref SplitNodes adaptor.
    1.83  #ifdef DOXYGEN
    1.84 -  template <typename GR, typename LEN>
    1.85 +  template <typename GR, typename LEN, typename TR>
    1.86  #else
    1.87    template < typename GR,
    1.88 -             typename LEN = typename GR::template ArcMap<int> >
    1.89 +             typename LEN = typename GR::template ArcMap<int>,
    1.90 +             typename TR = SuurballeDefaultTraits<GR, LEN> >
    1.91  #endif
    1.92    class Suurballe
    1.93    {
    1.94 @@ -74,26 +119,26 @@
    1.95  
    1.96    public:
    1.97  
    1.98 -    /// The type of the digraph the algorithm runs on.
    1.99 -    typedef GR Digraph;
   1.100 +    /// The type of the digraph.
   1.101 +    typedef typename TR::Digraph Digraph;
   1.102      /// The type of the length map.
   1.103 -    typedef LEN LengthMap;
   1.104 +    typedef typename TR::LengthMap LengthMap;
   1.105      /// The type of the lengths.
   1.106 -    typedef typename LengthMap::Value Length;
   1.107 -#ifdef DOXYGEN
   1.108 +    typedef typename TR::Length Length;
   1.109 +
   1.110      /// The type of the flow map.
   1.111 -    typedef GR::ArcMap<int> FlowMap;
   1.112 +    typedef typename TR::FlowMap FlowMap;
   1.113      /// The type of the potential map.
   1.114 -    typedef GR::NodeMap<Length> PotentialMap;
   1.115 -#else
   1.116 -    /// The type of the flow map.
   1.117 -    typedef typename Digraph::template ArcMap<int> FlowMap;
   1.118 -    /// The type of the potential map.
   1.119 -    typedef typename Digraph::template NodeMap<Length> PotentialMap;
   1.120 -#endif
   1.121 +    typedef typename TR::PotentialMap PotentialMap;
   1.122 +    /// The type of the path structures.
   1.123 +    typedef typename TR::Path Path;
   1.124 +    /// The cross reference type used for the heap.
   1.125 +    typedef typename TR::HeapCrossRef HeapCrossRef;
   1.126 +    /// The heap type used for internal Dijkstra computations.
   1.127 +    typedef typename TR::Heap Heap;
   1.128  
   1.129 -    /// The type of the path structures.
   1.130 -    typedef SimplePath<GR> Path;
   1.131 +    /// The \ref SuurballeDefaultTraits "traits class" of the algorithm.
   1.132 +    typedef TR Traits;
   1.133  
   1.134    private:
   1.135  
   1.136 @@ -104,44 +149,38 @@
   1.137      // distance of the nodes.
   1.138      class ResidualDijkstra
   1.139      {
   1.140 -      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
   1.141 -      typedef BinHeap<Length, HeapCrossRef> Heap;
   1.142 +    private:
   1.143 +
   1.144 +      const Digraph &_graph;
   1.145 +      const LengthMap &_length;
   1.146 +      const FlowMap &_flow;
   1.147 +      PotentialMap &_pi;
   1.148 +      PredMap &_pred;
   1.149 +      Node _s;
   1.150 +      Node _t;
   1.151 +
   1.152 +      PotentialMap _dist;
   1.153 +      std::vector<Node> _proc_nodes;
   1.154 +
   1.155 +    public:
   1.156 +
   1.157 +      // Constructor
   1.158 +      ResidualDijkstra(Suurballe &srb) :
   1.159 +        _graph(srb._graph), _length(srb._length),
   1.160 +        _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred),
   1.161 +        _s(srb._s), _t(srb._t), _dist(_graph) {}
   1.162 +
   1.163 +      // Run the algorithm and return true if a path is found
   1.164 +      // from the source node to the target node.
   1.165 +      bool run(int cnt) {
   1.166 +        return cnt == 0 ? startFirst() : start();
   1.167 +      }
   1.168  
   1.169      private:
   1.170  
   1.171 -      // The digraph the algorithm runs on
   1.172 -      const Digraph &_graph;
   1.173 -
   1.174 -      // The main maps
   1.175 -      const FlowMap &_flow;
   1.176 -      const LengthMap &_length;
   1.177 -      PotentialMap &_potential;
   1.178 -
   1.179 -      // The distance map
   1.180 -      PotentialMap _dist;
   1.181 -      // The pred arc map
   1.182 -      PredMap &_pred;
   1.183 -      // The processed (i.e. permanently labeled) nodes
   1.184 -      std::vector<Node> _proc_nodes;
   1.185 -
   1.186 -      Node _s;
   1.187 -      Node _t;
   1.188 -
   1.189 -    public:
   1.190 -
   1.191 -      /// Constructor.
   1.192 -      ResidualDijkstra( const Digraph &graph,
   1.193 -                        const FlowMap &flow,
   1.194 -                        const LengthMap &length,
   1.195 -                        PotentialMap &potential,
   1.196 -                        PredMap &pred,
   1.197 -                        Node s, Node t ) :
   1.198 -        _graph(graph), _flow(flow), _length(length), _potential(potential),
   1.199 -        _dist(graph), _pred(pred), _s(s), _t(t) {}
   1.200 -
   1.201 -      /// \brief Run the algorithm. It returns \c true if a path is found
   1.202 -      /// from the source node to the target node.
   1.203 -      bool run() {
   1.204 +      // Execute the algorithm for the first time (the flow and potential
   1.205 +      // functions have to be identically zero).
   1.206 +      bool startFirst() {
   1.207          HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
   1.208          Heap heap(heap_cross_ref);
   1.209          heap.push(_s, 0);
   1.210 @@ -151,29 +190,74 @@
   1.211          // Process nodes
   1.212          while (!heap.empty() && heap.top() != _t) {
   1.213            Node u = heap.top(), v;
   1.214 -          Length d = heap.prio() + _potential[u], nd;
   1.215 +          Length d = heap.prio(), dn;
   1.216            _dist[u] = heap.prio();
   1.217 +          _proc_nodes.push_back(u);
   1.218            heap.pop();
   1.219 +
   1.220 +          // Traverse outgoing arcs
   1.221 +          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
   1.222 +            v = _graph.target(e);
   1.223 +            switch(heap.state(v)) {
   1.224 +              case Heap::PRE_HEAP:
   1.225 +                heap.push(v, d + _length[e]);
   1.226 +                _pred[v] = e;
   1.227 +                break;
   1.228 +              case Heap::IN_HEAP:
   1.229 +                dn = d + _length[e];
   1.230 +                if (dn < heap[v]) {
   1.231 +                  heap.decrease(v, dn);
   1.232 +                  _pred[v] = e;
   1.233 +                }
   1.234 +                break;
   1.235 +              case Heap::POST_HEAP:
   1.236 +                break;
   1.237 +            }
   1.238 +          }
   1.239 +        }
   1.240 +        if (heap.empty()) return false;
   1.241 +
   1.242 +        // Update potentials of processed nodes
   1.243 +        Length t_dist = heap.prio();
   1.244 +        for (int i = 0; i < int(_proc_nodes.size()); ++i)
   1.245 +          _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist;
   1.246 +        return true;
   1.247 +      }
   1.248 +
   1.249 +      // Execute the algorithm.
   1.250 +      bool start() {
   1.251 +        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
   1.252 +        Heap heap(heap_cross_ref);
   1.253 +        heap.push(_s, 0);
   1.254 +        _pred[_s] = INVALID;
   1.255 +        _proc_nodes.clear();
   1.256 +
   1.257 +        // Process nodes
   1.258 +        while (!heap.empty() && heap.top() != _t) {
   1.259 +          Node u = heap.top(), v;
   1.260 +          Length d = heap.prio() + _pi[u], dn;
   1.261 +          _dist[u] = heap.prio();
   1.262            _proc_nodes.push_back(u);
   1.263 +          heap.pop();
   1.264  
   1.265            // Traverse outgoing arcs
   1.266            for (OutArcIt e(_graph, u); e != INVALID; ++e) {
   1.267              if (_flow[e] == 0) {
   1.268                v = _graph.target(e);
   1.269                switch(heap.state(v)) {
   1.270 -              case Heap::PRE_HEAP:
   1.271 -                heap.push(v, d + _length[e] - _potential[v]);
   1.272 -                _pred[v] = e;
   1.273 -                break;
   1.274 -              case Heap::IN_HEAP:
   1.275 -                nd = d + _length[e] - _potential[v];
   1.276 -                if (nd < heap[v]) {
   1.277 -                  heap.decrease(v, nd);
   1.278 +                case Heap::PRE_HEAP:
   1.279 +                  heap.push(v, d + _length[e] - _pi[v]);
   1.280                    _pred[v] = e;
   1.281 -                }
   1.282 -                break;
   1.283 -              case Heap::POST_HEAP:
   1.284 -                break;
   1.285 +                  break;
   1.286 +                case Heap::IN_HEAP:
   1.287 +                  dn = d + _length[e] - _pi[v];
   1.288 +                  if (dn < heap[v]) {
   1.289 +                    heap.decrease(v, dn);
   1.290 +                    _pred[v] = e;
   1.291 +                  }
   1.292 +                  break;
   1.293 +                case Heap::POST_HEAP:
   1.294 +                  break;
   1.295                }
   1.296              }
   1.297            }
   1.298 @@ -183,19 +267,19 @@
   1.299              if (_flow[e] == 1) {
   1.300                v = _graph.source(e);
   1.301                switch(heap.state(v)) {
   1.302 -              case Heap::PRE_HEAP:
   1.303 -                heap.push(v, d - _length[e] - _potential[v]);
   1.304 -                _pred[v] = e;
   1.305 -                break;
   1.306 -              case Heap::IN_HEAP:
   1.307 -                nd = d - _length[e] - _potential[v];
   1.308 -                if (nd < heap[v]) {
   1.309 -                  heap.decrease(v, nd);
   1.310 +                case Heap::PRE_HEAP:
   1.311 +                  heap.push(v, d - _length[e] - _pi[v]);
   1.312                    _pred[v] = e;
   1.313 -                }
   1.314 -                break;
   1.315 -              case Heap::POST_HEAP:
   1.316 -                break;
   1.317 +                  break;
   1.318 +                case Heap::IN_HEAP:
   1.319 +                  dn = d - _length[e] - _pi[v];
   1.320 +                  if (dn < heap[v]) {
   1.321 +                    heap.decrease(v, dn);
   1.322 +                    _pred[v] = e;
   1.323 +                  }
   1.324 +                  break;
   1.325 +                case Heap::POST_HEAP:
   1.326 +                  break;
   1.327                }
   1.328              }
   1.329            }
   1.330 @@ -205,12 +289,89 @@
   1.331          // Update potentials of processed nodes
   1.332          Length t_dist = heap.prio();
   1.333          for (int i = 0; i < int(_proc_nodes.size()); ++i)
   1.334 -          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
   1.335 +          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
   1.336          return true;
   1.337        }
   1.338  
   1.339      }; //class ResidualDijkstra
   1.340  
   1.341 +  public:
   1.342 +
   1.343 +    /// \name Named Template Parameters
   1.344 +    /// @{
   1.345 +
   1.346 +    template <typename T>
   1.347 +    struct SetFlowMapTraits : public Traits {
   1.348 +      typedef T FlowMap;
   1.349 +    };
   1.350 +
   1.351 +    /// \brief \ref named-templ-param "Named parameter" for setting
   1.352 +    /// \c FlowMap type.
   1.353 +    ///
   1.354 +    /// \ref named-templ-param "Named parameter" for setting
   1.355 +    /// \c FlowMap type.
   1.356 +    template <typename T>
   1.357 +    struct SetFlowMap
   1.358 +      : public Suurballe<GR, LEN, SetFlowMapTraits<T> > {
   1.359 +      typedef Suurballe<GR, LEN, SetFlowMapTraits<T> > Create;
   1.360 +    };
   1.361 +
   1.362 +    template <typename T>
   1.363 +    struct SetPotentialMapTraits : public Traits {
   1.364 +      typedef T PotentialMap;
   1.365 +    };
   1.366 +
   1.367 +    /// \brief \ref named-templ-param "Named parameter" for setting
   1.368 +    /// \c PotentialMap type.
   1.369 +    ///
   1.370 +    /// \ref named-templ-param "Named parameter" for setting
   1.371 +    /// \c PotentialMap type.
   1.372 +    template <typename T>
   1.373 +    struct SetPotentialMap
   1.374 +      : public Suurballe<GR, LEN, SetPotentialMapTraits<T> > {
   1.375 +      typedef Suurballe<GR, LEN, SetPotentialMapTraits<T> > Create;
   1.376 +    };
   1.377 +
   1.378 +    template <typename T>
   1.379 +    struct SetPathTraits : public Traits {
   1.380 +      typedef T Path;
   1.381 +    };
   1.382 +
   1.383 +    /// \brief \ref named-templ-param "Named parameter" for setting
   1.384 +    /// \c %Path type.
   1.385 +    ///
   1.386 +    /// \ref named-templ-param "Named parameter" for setting \c %Path type.
   1.387 +    /// It must conform to the \ref lemon::concepts::Path "Path" concept
   1.388 +    /// and it must have an \c addBack() function.
   1.389 +    template <typename T>
   1.390 +    struct SetPath
   1.391 +      : public Suurballe<GR, LEN, SetPathTraits<T> > {
   1.392 +      typedef Suurballe<GR, LEN, SetPathTraits<T> > Create;
   1.393 +    };
   1.394 +
   1.395 +    template <typename H, typename CR>
   1.396 +    struct SetHeapTraits : public Traits {
   1.397 +      typedef H Heap;
   1.398 +      typedef CR HeapCrossRef;
   1.399 +    };
   1.400 +
   1.401 +    /// \brief \ref named-templ-param "Named parameter" for setting
   1.402 +    /// \c Heap and \c HeapCrossRef types.
   1.403 +    ///
   1.404 +    /// \ref named-templ-param "Named parameter" for setting \c Heap
   1.405 +    /// and \c HeapCrossRef types with automatic allocation.
   1.406 +    /// They will be used for internal Dijkstra computations.
   1.407 +    /// The heap type must conform to the \ref lemon::concepts::Heap "Heap"
   1.408 +    /// concept and its priority type must be \c Length.
   1.409 +    template <typename H,
   1.410 +              typename CR = typename Digraph::template NodeMap<int> >
   1.411 +    struct SetHeap
   1.412 +      : public Suurballe<GR, LEN, SetHeapTraits<H, CR> > {
   1.413 +      typedef Suurballe<GR, LEN, SetHeapTraits<H, CR> > Create;
   1.414 +    };
   1.415 +
   1.416 +    /// @}
   1.417 +
   1.418    private:
   1.419  
   1.420      // The digraph the algorithm runs on
   1.421 @@ -226,19 +387,25 @@
   1.422      bool _local_potential;
   1.423  
   1.424      // The source node
   1.425 -    Node _source;
   1.426 +    Node _s;
   1.427      // The target node
   1.428 -    Node _target;
   1.429 +    Node _t;
   1.430  
   1.431      // Container to store the found paths
   1.432 -    std::vector< SimplePath<Digraph> > paths;
   1.433 +    std::vector<Path> _paths;
   1.434      int _path_num;
   1.435  
   1.436      // The pred arc map
   1.437      PredMap _pred;
   1.438 -    // Implementation of the Dijkstra algorithm for finding augmenting
   1.439 -    // shortest paths in the residual network
   1.440 -    ResidualDijkstra *_dijkstra;
   1.441 +
   1.442 +    // Data for full init
   1.443 +    PotentialMap *_init_dist;
   1.444 +    PredMap *_init_pred;
   1.445 +    bool _full_init;
   1.446 +
   1.447 +  protected:
   1.448 +
   1.449 +    Suurballe() {}
   1.450  
   1.451    public:
   1.452  
   1.453 @@ -251,14 +418,16 @@
   1.454      Suurballe( const Digraph &graph,
   1.455                 const LengthMap &length ) :
   1.456        _graph(graph), _length(length), _flow(0), _local_flow(false),
   1.457 -      _potential(0), _local_potential(false), _pred(graph)
   1.458 +      _potential(0), _local_potential(false), _pred(graph),
   1.459 +      _init_dist(0), _init_pred(0)
   1.460      {}
   1.461  
   1.462      /// Destructor.
   1.463      ~Suurballe() {
   1.464        if (_local_flow) delete _flow;
   1.465        if (_local_potential) delete _potential;
   1.466 -      delete _dijkstra;
   1.467 +      delete _init_dist;
   1.468 +      delete _init_pred;
   1.469      }
   1.470  
   1.471      /// \brief Set the flow map.
   1.472 @@ -303,10 +472,13 @@
   1.473  
   1.474      /// \name Execution Control
   1.475      /// The simplest way to execute the algorithm is to call the run()
   1.476 -    /// function.
   1.477 -    /// \n
   1.478 +    /// function.\n
   1.479 +    /// If you need to execute the algorithm many times using the same
   1.480 +    /// source node, then you may call fullInit() once and start()
   1.481 +    /// for each target node.\n
   1.482      /// If you only need the flow that is the union of the found
   1.483 -    /// arc-disjoint paths, you may call init() and findFlow().
   1.484 +    /// arc-disjoint paths, then you may call findFlow() instead of
   1.485 +    /// start().
   1.486  
   1.487      /// @{
   1.488  
   1.489 @@ -326,23 +498,21 @@
   1.490      /// just a shortcut of the following code.
   1.491      /// \code
   1.492      ///   s.init(s);
   1.493 -    ///   s.findFlow(t, k);
   1.494 -    ///   s.findPaths();
   1.495 +    ///   s.start(t, k);
   1.496      /// \endcode
   1.497      int run(const Node& s, const Node& t, int k = 2) {
   1.498        init(s);
   1.499 -      findFlow(t, k);
   1.500 -      findPaths();
   1.501 +      start(t, k);
   1.502        return _path_num;
   1.503      }
   1.504  
   1.505      /// \brief Initialize the algorithm.
   1.506      ///
   1.507 -    /// This function initializes the algorithm.
   1.508 +    /// This function initializes the algorithm with the given source node.
   1.509      ///
   1.510      /// \param s The source node.
   1.511      void init(const Node& s) {
   1.512 -      _source = s;
   1.513 +      _s = s;
   1.514  
   1.515        // Initialize maps
   1.516        if (!_flow) {
   1.517 @@ -353,8 +523,63 @@
   1.518          _potential = new PotentialMap(_graph);
   1.519          _local_potential = true;
   1.520        }
   1.521 -      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
   1.522 -      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
   1.523 +      _full_init = false;
   1.524 +    }
   1.525 +
   1.526 +    /// \brief Initialize the algorithm and perform Dijkstra.
   1.527 +    ///
   1.528 +    /// This function initializes the algorithm and performs a full
   1.529 +    /// Dijkstra search from the given source node. It makes consecutive
   1.530 +    /// executions of \ref start() "start(t, k)" faster, since they
   1.531 +    /// have to perform %Dijkstra only k-1 times.
   1.532 +    ///
   1.533 +    /// This initialization is usually worth using instead of \ref init()
   1.534 +    /// if the algorithm is executed many times using the same source node.
   1.535 +    ///
   1.536 +    /// \param s The source node.
   1.537 +    void fullInit(const Node& s) {
   1.538 +      // Initialize maps
   1.539 +      init(s);
   1.540 +      if (!_init_dist) {
   1.541 +        _init_dist = new PotentialMap(_graph);
   1.542 +      }
   1.543 +      if (!_init_pred) {
   1.544 +        _init_pred = new PredMap(_graph);
   1.545 +      }
   1.546 +
   1.547 +      // Run a full Dijkstra
   1.548 +      typename Dijkstra<Digraph, LengthMap>
   1.549 +        ::template SetStandardHeap<Heap>
   1.550 +        ::template SetDistMap<PotentialMap>
   1.551 +        ::template SetPredMap<PredMap>
   1.552 +        ::Create dijk(_graph, _length);
   1.553 +      dijk.distMap(*_init_dist).predMap(*_init_pred);
   1.554 +      dijk.run(s);
   1.555 +
   1.556 +      _full_init = true;
   1.557 +    }
   1.558 +
   1.559 +    /// \brief Execute the algorithm.
   1.560 +    ///
   1.561 +    /// This function executes the algorithm.
   1.562 +    ///
   1.563 +    /// \param t The target node.
   1.564 +    /// \param k The number of paths to be found.
   1.565 +    ///
   1.566 +    /// \return \c k if there are at least \c k arc-disjoint paths from
   1.567 +    /// \c s to \c t in the digraph. Otherwise it returns the number of
   1.568 +    /// arc-disjoint paths found.
   1.569 +    ///
   1.570 +    /// \note Apart from the return value, <tt>s.start(t, k)</tt> is
   1.571 +    /// just a shortcut of the following code.
   1.572 +    /// \code
   1.573 +    ///   s.findFlow(t, k);
   1.574 +    ///   s.findPaths();
   1.575 +    /// \endcode
   1.576 +    int start(const Node& t, int k = 2) {
   1.577 +      findFlow(t, k);
   1.578 +      findPaths();
   1.579 +      return _path_num;
   1.580      }
   1.581  
   1.582      /// \brief Execute the algorithm to find an optimal flow.
   1.583 @@ -372,20 +597,39 @@
   1.584      ///
   1.585      /// \pre \ref init() must be called before using this function.
   1.586      int findFlow(const Node& t, int k = 2) {
   1.587 -      _target = t;
   1.588 -      _dijkstra =
   1.589 -        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
   1.590 -                              _source, _target );
   1.591 +      _t = t;
   1.592 +      ResidualDijkstra dijkstra(*this);
   1.593 +
   1.594 +      // Initialization
   1.595 +      for (ArcIt e(_graph); e != INVALID; ++e) {
   1.596 +        (*_flow)[e] = 0;
   1.597 +      }
   1.598 +      if (_full_init) {
   1.599 +        for (NodeIt n(_graph); n != INVALID; ++n) {
   1.600 +          (*_potential)[n] = (*_init_dist)[n];
   1.601 +        }
   1.602 +        Node u = _t;
   1.603 +        Arc e;
   1.604 +        while ((e = (*_init_pred)[u]) != INVALID) {
   1.605 +          (*_flow)[e] = 1;
   1.606 +          u = _graph.source(e);
   1.607 +        }
   1.608 +        _path_num = 1;
   1.609 +      } else {
   1.610 +        for (NodeIt n(_graph); n != INVALID; ++n) {
   1.611 +          (*_potential)[n] = 0;
   1.612 +        }
   1.613 +        _path_num = 0;
   1.614 +      }
   1.615  
   1.616        // Find shortest paths
   1.617 -      _path_num = 0;
   1.618        while (_path_num < k) {
   1.619          // Run Dijkstra
   1.620 -        if (!_dijkstra->run()) break;
   1.621 +        if (!dijkstra.run(_path_num)) break;
   1.622          ++_path_num;
   1.623  
   1.624          // Set the flow along the found shortest path
   1.625 -        Node u = _target;
   1.626 +        Node u = _t;
   1.627          Arc e;
   1.628          while ((e = _pred[u]) != INVALID) {
   1.629            if (u == _graph.target(e)) {
   1.630 @@ -402,8 +646,8 @@
   1.631  
   1.632      /// \brief Compute the paths from the flow.
   1.633      ///
   1.634 -    /// This function computes the paths from the found minimum cost flow,
   1.635 -    /// which is the union of some arc-disjoint paths.
   1.636 +    /// This function computes arc-disjoint paths from the found minimum
   1.637 +    /// cost flow, which is the union of them.
   1.638      ///
   1.639      /// \pre \ref init() and \ref findFlow() must be called before using
   1.640      /// this function.
   1.641 @@ -411,15 +655,15 @@
   1.642        FlowMap res_flow(_graph);
   1.643        for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
   1.644  
   1.645 -      paths.clear();
   1.646 -      paths.resize(_path_num);
   1.647 +      _paths.clear();
   1.648 +      _paths.resize(_path_num);
   1.649        for (int i = 0; i < _path_num; ++i) {
   1.650 -        Node n = _source;
   1.651 -        while (n != _target) {
   1.652 +        Node n = _s;
   1.653 +        while (n != _t) {
   1.654            OutArcIt e(_graph, n);
   1.655            for ( ; res_flow[e] == 0; ++e) ;
   1.656            n = _graph.target(e);
   1.657 -          paths[i].addBack(e);
   1.658 +          _paths[i].addBack(e);
   1.659            res_flow[e] = 0;
   1.660          }
   1.661        }
   1.662 @@ -518,7 +762,7 @@
   1.663      /// \pre \ref run() or \ref findPaths() must be called before using
   1.664      /// this function.
   1.665      const Path& path(int i) const {
   1.666 -      return paths[i];
   1.667 +      return _paths[i];
   1.668      }
   1.669  
   1.670      /// @}