COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/suurballe.h @ 2276:1a8a66b6c6ce

Last change on this file since 2276:1a8a66b6c6ce was 2276:1a8a66b6c6ce, checked in by Balazs Dezso, 13 years ago

Min cost flow is renamed to SspMinCostFlow?

File size: 6.4 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_SUURBALLE_H
20#define LEMON_SUURBALLE_H
21
22///\ingroup flowalgs
23///\file
24///\brief An algorithm for finding k paths of minimal total length.
25
26
27#include <lemon/maps.h>
28#include <vector>
29#include <lemon/ssp_min_cost_flow.h>
30
31namespace lemon {
32
33/// \addtogroup flowalgs
34/// @{
35
36  ///\brief Implementation of an algorithm for finding k edge-disjoint
37  /// paths between 2 nodes of minimal total length
38  ///
39  /// The class \ref lemon::Suurballe implements
40  /// an algorithm for finding k edge-disjoint paths
41  /// from a given source node to a given target node in an
42  /// edge-weighted directed graph having minimal total weight (length).
43  ///
44  ///\warning Length values should be nonnegative!
45  ///
46  ///\param Graph The directed graph type the algorithm runs on.
47  ///\param LengthMap The type of the length map (values should be nonnegative).
48  ///
49  ///\note It it questionable whether it is correct to call this method after
50  ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm
51  ///for finding minimum cost flows. In fact, this implementation just
52  ///wraps the SspMinCostFlow algorithms. The paper of both %Suurballe and
53  ///Edmonds-Karp published in 1972, therefore it is possibly right to
54  ///state that they are
55  ///independent results. Most frequently this special case is referred as
56  ///%Suurballe method in the literature, especially in communication
57  ///network context.
58  ///\author Attila Bernath
59  template <typename Graph, typename LengthMap>
60  class Suurballe{
61
62
63    typedef typename LengthMap::Value Length;
64   
65    typedef typename Graph::Node Node;
66    typedef typename Graph::NodeIt NodeIt;
67    typedef typename Graph::Edge Edge;
68    typedef typename Graph::OutEdgeIt OutEdgeIt;
69    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
70
71    typedef ConstMap<Edge,int> ConstMap;
72
73    const Graph& G;
74
75    Node s;
76    Node t;
77
78    //Auxiliary variables
79    //This is the capacity map for the mincostflow problem
80    ConstMap const1map;
81    //This MinCostFlow instance will actually solve the problem
82    SspMinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;
83
84    //Container to store found paths
85    std::vector< std::vector<Edge> > paths;
86
87  public :
88
89
90    /// \brief The constructor of the class.
91    ///
92    /// \param _G The directed graph the algorithm runs on.
93    /// \param _length The length (weight or cost) of the edges.
94    /// \param _s Source node.
95    /// \param _t Target node.
96    Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) :
97      G(_G), s(_s), t(_t), const1map(1),
98      min_cost_flow(_G, _length, const1map, _s, _t) { }
99
100    /// \brief Runs the algorithm.
101    ///
102    /// Runs the algorithm.
103    /// Returns k if there are at least k edge-disjoint paths from s to t.
104    /// Otherwise it returns the number of edge-disjoint paths found
105    /// from s to t.
106    ///
107    /// \param k How many paths are we looking for?
108    ///
109    int run(int k) {
110      int i = min_cost_flow.run(k);
111
112      //Let's find the paths
113      //We put the paths into stl vectors (as an inner representation).
114      //In the meantime we lose the information stored in 'reversed'.
115      //We suppose the lengths to be positive now.
116
117      //We don't want to change the flow of min_cost_flow, so we make a copy
118      //The name here suggests that the flow has only 0/1 values.
119      EdgeIntMap reversed(G);
120
121      for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
122        reversed[e] = min_cost_flow.getFlow()[e];
123     
124      paths.clear();
125      paths.resize(k);
126      for (int j=0; j<i; ++j){
127        Node n=s;
128
129        while (n!=t){
130
131          OutEdgeIt e(G, n);
132         
133          while (!reversed[e]){
134            ++e;
135          }
136          n = G.target(e);
137          paths[j].push_back(e);
138          reversed[e] = 1-reversed[e];
139        }
140       
141      }
142      return i;
143    }
144
145   
146    /// \brief Returns the total length of the paths.
147    ///
148    /// This function gives back the total length of the found paths.
149    Length totalLength(){
150      return min_cost_flow.totalLength();
151    }
152
153    /// \brief Returns the found flow.
154    ///
155    /// This function returns a const reference to the EdgeMap \c flow.
156    const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
157
158    /// \brief Returns the optimal dual solution
159    ///
160    /// This function returns a const reference to the NodeMap \c
161    /// potential (the dual solution).
162    const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
163
164    /// \brief Checks whether the complementary slackness holds.
165    ///
166    /// This function checks, whether the given solution is optimal.
167    /// Currently this function only checks optimality, doesn't bother
168    /// with feasibility.  It is meant for testing purposes.
169    bool checkComplementarySlackness(){
170      return min_cost_flow.checkComplementarySlackness();
171    }
172
173    /// \brief Read the found paths.
174    ///
175    /// This function gives back the \c j-th path in argument p.
176    /// Assumes that \c run() has been run and nothing has changed
177    /// since then.
178    ///
179    /// \warning It is assumed that \c p is constructed to be a path
180    /// of graph \c G.  If \c j is not less than the result of
181    /// previous \c run, then the result here will be an empty path
182    /// (\c j can be 0 as well).
183    ///
184    /// \param Path The type of the path structure to put the result
185    /// to (must meet lemon path concept).
186    /// \param p The path to put the result to.
187    /// \param j Which path you want to get from the found paths (in a
188    /// real application you would get the found paths iteratively).
189    template<typename Path>
190    void getPath(Path& p, size_t j){
191
192      p.clear();
193      if (j>paths.size()-1){
194        return;
195      }
196      typename Path::Builder B(p);
197      for(typename std::vector<Edge>::iterator i=paths[j].begin();
198          i!=paths[j].end(); ++i ){
199        B.pushBack(*i);
200      }
201
202      B.commit();
203    }
204
205  }; //class Suurballe
206
207  ///@}
208
209} //namespace lemon
210
211#endif //LEMON_SUURBALLE_H
Note: See TracBrowser for help on using the repository browser.