diff -r c6acc34f98dc -r 1a7fe3bef514 lemon/suurballe.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/suurballe.h	Thu Nov 05 15:50:01 2009 +0100
@@ -0,0 +1,535 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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 <vector>
+#include <limits>
+#include <lemon/bin_heap.h>
+#include <lemon/path.h>
+#include <lemon/list_graph.h>
+#include <lemon/maps.h>
+
+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.
+  ///
+  /// Note that this problem is a special case of the \ref min_cost_flow
+  /// "minimum cost flow problem". This implementation is actually an
+  /// efficient specialized version of the \ref CapacityScaling
+  /// "Successive Shortest Path" algorithm directly for this problem.
+  /// Therefore this class provides query functions for flow values and
+  /// node potentials (the dual solution) just like the minimum cost flow
+  /// algorithms.
+  ///
+  /// \tparam GR The digraph type the algorithm runs on.
+  /// \tparam LEN The type of the length map.
+  /// The default value is <tt>GR::ArcMap<int></tt>.
+  ///
+  /// \warning Length values should be \e non-negative \e integers.
+  ///
+  /// \note For finding node-disjoint paths this algorithm can be used
+  /// along with the \ref SplitNodes adaptor.
+#ifdef DOXYGEN
+  template <typename GR, typename LEN>
+#else
+  template < typename GR,
+             typename LEN = typename GR::template ArcMap<int> >
+#endif
+  class Suurballe
+  {
+    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+    typedef ConstMap<Arc, int> ConstArcMap;
+    typedef typename GR::template NodeMap<Arc> PredMap;
+
+  public:
+
+    /// The type of the digraph the algorithm runs on.
+    typedef GR Digraph;
+    /// The type of the length map.
+    typedef LEN LengthMap;
+    /// The type of the lengths.
+    typedef typename LengthMap::Value Length;
+#ifdef DOXYGEN
+    /// The type of the flow map.
+    typedef GR::ArcMap<int> FlowMap;
+    /// The type of the potential map.
+    typedef GR::NodeMap<Length> PotentialMap;
+#else
+    /// The type of the flow map.
+    typedef typename Digraph::template ArcMap<int> FlowMap;
+    /// The type of the potential map.
+    typedef typename Digraph::template NodeMap<Length> PotentialMap;
+#endif
+
+    /// The type of the path structures.
+    typedef SimplePath<GR> Path;
+
+  private:
+
+    // ResidualDijkstra is a special implementation of the
+    // Dijkstra algorithm for finding shortest paths in the
+    // residual network 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<int> HeapCrossRef;
+      typedef BinHeap<Length, HeapCrossRef> 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<Node> _proc_nodes;
+
+      Node _s;
+      Node _t;
+
+    public:
+
+      /// Constructor.
+      ResidualDijkstra( const Digraph &graph,
+                        const FlowMap &flow,
+                        const LengthMap &length,
+                        PotentialMap &potential,
+                        PredMap &pred,
+                        Node s, Node t ) :
+        _graph(graph), _flow(flow), _length(length), _potential(potential),
+        _dist(graph), _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<Digraph> > 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 graph The digraph the algorithm runs on.
+    /// \param length The length (cost) values of the arcs.
+    Suurballe( const Digraph &graph,
+               const LengthMap &length ) :
+      _graph(graph), _length(length), _flow(0), _local_flow(false),
+      _potential(0), _local_potential(false), _pred(graph)
+    {
+      LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
+        "The length type of Suurballe must be integer");
+    }
+
+    /// 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.
+    /// If it is not used before calling \ref run() or \ref init(),
+    /// an instance will be allocated automatically. The destructor
+    /// deallocates this automatically allocated map, of course.
+    ///
+    /// The found flow contains only 0 and 1 values, since it is the
+    /// union of the found arc-disjoint paths.
+    ///
+    /// \return <tt>(*this)</tt>
+    Suurballe& flowMap(FlowMap &map) {
+      if (_local_flow) {
+        delete _flow;
+        _local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Set the potential map.
+    ///
+    /// This function sets the potential map.
+    /// If it is not used before calling \ref run() or \ref init(),
+    /// an instance will be allocated automatically. The destructor
+    /// deallocates this automatically allocated map, of course.
+    ///
+    /// The node potentials provide the dual solution of the underlying
+    /// \ref min_cost_flow "minimum cost flow problem".
+    ///
+    /// \return <tt>(*this)</tt>
+    Suurballe& potentialMap(PotentialMap &map) {
+      if (_local_potential) {
+        delete _potential;
+        _local_potential = false;
+      }
+      _potential = &map;
+      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 s The source node.
+    /// \param t The target node.
+    /// \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, <tt>s.run(s, t, k)</tt> is
+    /// just a shortcut of the following code.
+    /// \code
+    ///   s.init(s);
+    ///   s.findFlow(t, k);
+    ///   s.findPaths();
+    /// \endcode
+    int run(const Node& s, const Node& t, int k = 2) {
+      init(s);
+      findFlow(t, k);
+      findPaths();
+      return _path_num;
+    }
+
+    /// \brief Initialize the algorithm.
+    ///
+    /// This function initializes the algorithm.
+    ///
+    /// \param s The source node.
+    void init(const Node& s) {
+      _source = s;
+
+      // 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;
+    }
+
+    /// \brief Execute the 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.
+    ///
+    /// \param t The target node.
+    /// \param k The number of paths to be found.
+    ///
+    /// \return \c k if there are at least \c k arc-disjoint paths from
+    /// the source node to the given node \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(const Node& t, int k = 2) {
+      _target = t;
+      _dijkstra =
+        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
+                              _source, _target );
+
+      // 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 found minimum cost flow,
+    /// which is the union of some arc-disjoint paths.
+    ///
+    /// \pre \ref init() and \ref findFlow() must be called before using
+    /// this function.
+    void findPaths() {
+      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 the total length of the found paths.
+    ///
+    /// This function returns the total length of the found paths, i.e.
+    /// the total cost of the found flow.
+    /// The complexity of the function is O(e).
+    ///
+    /// \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 flow value on the given arc.
+    ///
+    /// This function returns the flow value on the given arc.
+    /// It is \c 1 if the arc is involved in one of the found arc-disjoint
+    /// 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 a const reference to an arc map storing the
+    /// found flow.
+    ///
+    /// This function returns a const reference to an 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 the potential of the given node.
+    ///
+    /// This function returns the potential of the given node.
+    /// The node potentials provide the dual solution of the
+    /// underlying \ref min_cost_flow "minimum cost flow problem".
+    ///
+    /// \pre \ref run() or \ref findFlow() must be called before using
+    /// this function.
+    Length potential(const Node& node) const {
+      return (*_potential)[node];
+    }
+
+    /// \brief Return a const reference to a node map storing the
+    /// found potentials (the dual solution).
+    ///
+    /// This function returns a const reference to a node map storing
+    /// the found potentials that provide the dual solution of the
+    /// underlying \ref min_cost_flow "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 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 <tt>i</tt>-th path.
+    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
+    ///
+    /// \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