COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/suurballe.h @ 2193:8057a4245685

Last change on this file since 2193:8057a4245685 was 1956:a055123339d5, checked in by Alpar Juttner, 14 years ago

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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/min_cost_flow.h>
30
31namespace lemon {
32
33/// \addtogroup flowalgs
34/// @{
35
36  ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes
37  /// 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 MinCostFlow 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    MinCostFlow<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    */
97    Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) :
98      G(_G), s(_s), t(_t), const1map(1),
99      min_cost_flow(_G, _length, const1map, _s, _t) { }
100
101    ///Runs the algorithm.
102
103    ///Runs the algorithm.
104    ///Returns k if there are at least k edge-disjoint paths from s to t.
105    ///Otherwise it returns the number of edge-disjoint paths found
106    ///from s to t.
107    ///
108    ///\param k How many paths are we looking for?
109    ///
110    int run(int k) {
111      int i = min_cost_flow.run(k);
112
113      //Let's find the paths
114      //We put the paths into stl vectors (as an inner representation).
115      //In the meantime we lose the information stored in 'reversed'.
116      //We suppose the lengths to be positive now.
117
118      //We don't want to change the flow of min_cost_flow, so we make a copy
119      //The name here suggests that the flow has only 0/1 values.
120      EdgeIntMap reversed(G);
121
122      for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
123        reversed[e] = min_cost_flow.getFlow()[e];
124     
125      paths.clear();
126      paths.resize(k);
127      for (int j=0; j<i; ++j){
128        Node n=s;
129
130        while (n!=t){
131
132          OutEdgeIt e(G, n);
133         
134          while (!reversed[e]){
135            ++e;
136          }
137          n = G.target(e);
138          paths[j].push_back(e);
139          reversed[e] = 1-reversed[e];
140        }
141       
142      }
143      return i;
144    }
145
146   
147    ///Returns the total length of the paths.
148   
149    ///This function gives back the total length of the found paths.
150    Length totalLength(){
151      return min_cost_flow.totalLength();
152    }
153
154    ///Returns the found flow.
155
156    ///This function returns a const reference to the EdgeMap \c flow.
157    const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
158
159    /// Returns the optimal dual solution
160   
161    ///This function returns a const reference to the NodeMap
162    ///\c potential (the dual solution).
163    const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
164
165    ///Checks whether the complementary slackness holds.
166
167    ///This function checks, whether the given solution is optimal.
168    ///Currently this function only checks optimality,
169    ///doesn't bother with feasibility.
170    ///It is meant for testing purposes.
171    bool checkComplementarySlackness(){
172      return min_cost_flow.checkComplementarySlackness();
173    }
174
175    ///Read the found paths.
176   
177    ///This function gives back the \c j-th path in argument p.
178    ///Assumes that \c run() has been run and nothing has changed since then.
179    /// \warning It is assumed that \c p is constructed to
180    ///be a path of graph \c G.
181    ///If \c j is not less than the result of previous \c run,
182    ///then the result here will be an empty path (\c j can be 0 as well).
183    ///
184    ///\param Path The type of the path structure to put the result to (must meet lemon path concept).
185    ///\param p The path to put the result to.
186    ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively).
187    template<typename Path>
188    void getPath(Path& p, size_t j){
189
190      p.clear();
191      if (j>paths.size()-1){
192        return;
193      }
194      typename Path::Builder B(p);
195      for(typename std::vector<Edge>::iterator i=paths[j].begin();
196          i!=paths[j].end(); ++i ){
197        B.pushBack(*i);
198      }
199
200      B.commit();
201    }
202
203  }; //class Suurballe
204
205  ///@}
206
207} //namespace lemon
208
209#endif //LEMON_SUURBALLE_H
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