RhodeCode

/* -*- 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 <vector>

#include <lemon/bin_heap.h>

#include <lemon/path.h>

namespace lemon {

  /// \addtogroup shortest_path

  /// @{

  /// \brief Implementation of an 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 directed

  /// digraph.

  ///

  /// In fact, this implementation is the specialization of the

  /// \ref CapacityScaling "successive shortest path" algorithm.

  ///

  /// \tparam Digraph The directed digraph type the algorithm runs on.

  /// \tparam LengthMap The type of the length (cost) map.

  ///

  /// \warning Length values should be \e non-negative \e integers.

  ///

  /// \note For finding node-disjoint paths this algorithm can be used

  /// with \ref SplitDigraphAdaptor.

  ///

  /// \author Attila Bernath and Peter Kovacs

  template < typename Digraph, 

             typename LengthMap = typename Digraph::template ArcMap<int> >

  class Suurballe

  {

    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

    typedef typename LengthMap::Value Length;

    typedef ConstMap<Arc, int> ConstArcMap;

    typedef typename Digraph::template NodeMap<Arc> PredMap;

  public:

    /// 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;

    /// The type of the path structures.

    typedef SimplePath<Digraph> Path;

  private:

    /// \brief Special implementation of the \ref 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<int> HeapCrossRef;

      typedef BinHeap<Length, HeapCrossRef> Heap;

    private:

      // The directed 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 &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 Runs the algorithm. 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();

        // Processing 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);

          // Traversing 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;

              }

            }

          }

          // Traversing 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;

        // Updating 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 directed 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 digraph The directed 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 Sets the flow map.

    ///

    /// 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 Sets the potential map.

    ///

    /// 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 Runs the algorithm.

    ///

    /// 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. Otherwise it returns the number of

    /// arc-disjoint paths found.

    ///

    /// \note Apart from the return value, <tt>s.run(k)</tt> 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 Initializes the algorithm.

    ///

    /// Initializes the algorithm.

    void init() {

      // Initializing 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 Executes the successive shortest path algorithm to find

    /// an optimal flow.

    ///

    /// 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. 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) {

      // Finding shortest paths

      _path_num = 0;

      while (_path_num < k) {

        // Running Dijkstra

        if (!_dijkstra->run()) break;

        ++_path_num;

        // Setting 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 Computes the paths from the flow.

    ///

    /// Computes the paths from the flow.

    ///

    /// \pre \ref init() and \ref findFlow() must be called before using

    /// this function.

    void findPaths() {

      // Creating 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 result of the algorithm can be obtained using these

    /// functions.

    /// \n The algorithm should be executed before using them.

    /// @{

    /// \brief Returns a const reference to the arc map storing the

    /// found flow.

    ///

    /// 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 findFlow() must be called before using this

    /// function.

    const FlowMap& flowMap() const {

      return *_flow;

    }

    /// \brief Returns a const reference to the node map storing the

    /// found potentials (the dual solution).

    ///

    /// 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 findFlow() must be called before using this

    /// function.

    const PotentialMap& potentialMap() const {

      return *_potential;

    }

    /// \brief Returns the flow on the given arc.

    ///

    /// 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 findFlow() must be called before using this

    /// function.

    int flow(const Arc& arc) const {

      return (*_flow)[arc];

    }

    /// \brief Returns the potential of the given node.

    ///

    /// Returns the potential of the given node.

    ///

    /// \pre \ref run() or findFlow() must be called before using this

    /// function.

    Length potential(const Node& node) const {

      return (*_potential)[node];

    }

    /// \brief Returns the total length (cost) of the found paths (flow).

    ///

    /// Returns the total length (cost) of the found paths (flow).

    /// The complexity of the function is \f$ O(e) \f$.

    ///

    /// \pre \ref run() or 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 Returns the number of the found paths.

    ///

    /// Returns the number of the found paths.

    ///

    /// \pre \ref run() or findFlow() must be called before using this

    /// function.

    int pathNum() const {

      return _path_num;

    }

    /// \brief Returns a const reference to the specified path.

    ///

    /// 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 <tt>%pathNum()-1</tt>.

    ///

    /// \pre \ref run() or findPaths() must be called before using this

    /// function.

    Path path(int i) const {

      return paths[i];

    }

    /// @}

  }; //class Suurballe

  ///@}

} //namespace lemon

#endif //LEMON_SUURBALLE_H

@nodes

label	supply1	supply2	supply3

1	0	20	27	

2	0	-4	0		

3	0	0	0	

4	0	0	0	

5	0	9	0	

6	0	-6	0	

7	0	0	0	

8	0	0	0	

9	0	3	0	

10	0	-2	0	

11	0	0	0		

12	0	-20	-27	

@arcs

		cost	capacity	lower1	lower2

1	2	70	11		0	8

1	3	150	3		0	1

1	4	80	15		0	2

2	8	80	12		0	0

3	5	140	5		0	3

4	6	60	10		0	1

4	7	80	2		0	0

4	8	110	3		0	0

5	7	60	14		0	0

5	11	120	12		0	0

6	3	0	3		0	0

6	9	140	4		0	0

6	10	90	8		0	0

7	1	30	5		0	0

8	12	60	16		0	4

9	12	50	6		0	0

10	12	70	13		0	5

10	2	100	7		0	0

10	7	60	10		0	0

11	10	20	14		0	6

12	11	30	10		0	0

@attributes

source	1

target	12

@end

/* -*- 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.

 *

 */

#include <iostream>

#include <fstream>

#include <lemon/list_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/path.h>

#include <lemon/suurballe.h>

#include "test_tools.h"

using namespace lemon;

// Checks the feasibility of the flow

template <typename Digraph, typename FlowMap>

bool checkFlow( const Digraph& gr, const FlowMap& flow, 

                typename Digraph::Node s, typename Digraph::Node t,

                int value )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  for (ArcIt e(gr); e != INVALID; ++e)

    if (!(flow[e] == 0 || flow[e] == 1)) return false;

  for (NodeIt n(gr); n != INVALID; ++n) {

    int sum = 0;

    for (OutArcIt e(gr, n); e != INVALID; ++e)

      sum += flow[e];

    for (InArcIt e(gr, n); e != INVALID; ++e)

      sum -= flow[e];

    if (n == s && sum != value) return false;

    if (n == t && sum != -value) return false;

    if (n != s && n != t && sum != 0) return false;

  }

  return true;

}

// Checks the optimalitiy of the flow

template < typename Digraph, typename CostMap, 

           typename FlowMap, typename PotentialMap >

bool checkOptimality( const Digraph& gr, const CostMap& cost,

                      const FlowMap& flow, const PotentialMap& pi )

{

  // Checking the Complementary Slackness optimality condition

  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  bool opt = true;

  for (ArcIt e(gr); e != INVALID; ++e) {

    typename CostMap::Value red_cost =

      cost[e] + pi[gr.source(e)] - pi[gr.target(e)];

    opt = (flow[e] == 0 && red_cost >= 0) ||

          (flow[e] == 1 && red_cost <= 0);

    if (!opt) break;

  }

  return opt;

}

// Checks a path

template < typename Digraph, typename Path >

bool checkPath( const Digraph& gr, const Path& path,

                typename Digraph::Node s, typename Digraph::Node t)

{

  // Checking the Complementary Slackness optimality condition

  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  Node n = s;

  for (int i = 0; i < path.length(); ++i) {

    if (gr.source(path.nth(i)) != n) return false;

    n = gr.target(path.nth(i));

  }

  return n == t;

}

int main()

{

  DIGRAPH_TYPEDEFS(ListDigraph);

  // Reading the test digraph

  ListDigraph digraph;

  ListDigraph::ArcMap<int> length(digraph);

  Node source, target;

  std::string fname;

  if(getenv("srcdir"))

    fname = std::string(getenv("srcdir"));

  else fname = ".";

  fname += "/test/min_cost_flow_test.lgf";

  std::ifstream input(fname.c_str());

  check(input, "Input file '" << fname << "' not found");

  DigraphReader<ListDigraph>(digraph, input).

    arcMap("cost", length).

    node("source", source).

    node("target", target).

    run();

  input.close();

  // Finding 2 paths

  {

    Suurballe<ListDigraph> suurballe(digraph, length, source, target);

    check(suurballe.run(2) == 2, "Wrong number of paths");

    check(checkFlow(digraph, suurballe.flowMap(), source, target, 2),

          "The flow is not feasible");

    check(suurballe.totalLength() == 510, "The flow is not optimal");

    check(checkOptimality(digraph, length, suurballe.flowMap(), 

                          suurballe.potentialMap()),

          "Wrong potentials");

    for (int i = 0; i < suurballe.pathNum(); ++i)

      check(checkPath(digraph, suurballe.path(i), source, target),

            "Wrong path");

  }

  // Finding 3 paths

  {

    Suurballe<ListDigraph> suurballe(digraph, length, source, target);

    check(suurballe.run(3) == 3, "Wrong number of paths");

    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),

          "The flow is not feasible");

    check(suurballe.totalLength() == 1040, "The flow is not optimal");

    check(checkOptimality(digraph, length, suurballe.flowMap(), 

                          suurballe.potentialMap()),

          "Wrong potentials");

    for (int i = 0; i < suurballe.pathNum(); ++i)

      check(checkPath(digraph, suurballe.path(i), source, target),

            "Wrong path");

  }

  // Finding 5 paths (only 3 can be found)

  {

    Suurballe<ListDigraph> suurballe(digraph, length, source, target);

    check(suurballe.run(5) == 3, "Wrong number of paths");

    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),

          "The flow is not feasible");

    check(suurballe.totalLength() == 1040, "The flow is not optimal");

    check(checkOptimality(digraph, length, suurballe.flowMap(), 

                          suurballe.potentialMap()),

          "Wrong potentials");

    for (int i = 0; i < suurballe.pathNum(); ++i)

      check(checkPath(digraph, suurballe.path(i), source, target),

            "Wrong path");

  }

  return 0;

}

	lemon/suurballe.h \

	test/CMakeLists.txt \

        test/min_cost_flow_test.lgf

        test/suurballe_test \

test_suurballe_test_SOURCES = test/suurballe_test.cc