COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/suurballe.h @ 1875:98698b69a902

Last change on this file since 1875:98698b69a902 was 1875:98698b69a902, checked in by Alpar Juttner, 14 years ago

Happy new year to LEMON

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1/* -*- C++ -*-
2 * lemon/suurballe.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_SUURBALLE_H
18#define LEMON_SUURBALLE_H
19
20///\ingroup flowalgs
21///\file
22///\brief An algorithm for finding k paths of minimal total length.
23
24
25#include <lemon/maps.h>
26#include <vector>
27#include <lemon/min_cost_flow.h>
28
29namespace lemon {
30
31/// \addtogroup flowalgs
32/// @{
33
34  ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes
35  /// of minimal total length
36  ///
37  /// The class \ref lemon::Suurballe implements
38  /// an algorithm for finding k edge-disjoint paths
39  /// from a given source node to a given target node in an
40  /// edge-weighted directed graph having minimal total weight (length).
41  ///
42  ///\warning Length values should be nonnegative!
43  ///
44  ///\param Graph The directed graph type the algorithm runs on.
45  ///\param LengthMap The type of the length map (values should be nonnegative).
46  ///
47  ///\note It it questionable whether it is correct to call this method after
48  ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm
49  ///for finding minimum cost flows. In fact, this implementation just
50  ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and
51  ///Edmonds-Karp published in 1972, therefore it is possibly right to
52  ///state that they are
53  ///independent results. Most frequently this special case is referred as
54  ///%Suurballe method in the literature, especially in communication
55  ///network context.
56  ///\author Attila Bernath
57  template <typename Graph, typename LengthMap>
58  class Suurballe{
59
60
61    typedef typename LengthMap::Value Length;
62   
63    typedef typename Graph::Node Node;
64    typedef typename Graph::NodeIt NodeIt;
65    typedef typename Graph::Edge Edge;
66    typedef typename Graph::OutEdgeIt OutEdgeIt;
67    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
68
69    typedef ConstMap<Edge,int> ConstMap;
70
71    const Graph& G;
72
73    Node s;
74    Node t;
75
76    //Auxiliary variables
77    //This is the capacity map for the mincostflow problem
78    ConstMap const1map;
79    //This MinCostFlow instance will actually solve the problem
80    MinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;
81
82    //Container to store found paths
83    std::vector< std::vector<Edge> > paths;
84
85  public :
86
87
88    /*! \brief The constructor of the class.
89   
90    \param _G The directed graph the algorithm runs on.
91    \param _length The length (weight or cost) of the edges.
92    \param _s Source node.
93    \param _t Target node.
94    */
95    Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) :
96      G(_G), s(_s), t(_t), const1map(1),
97      min_cost_flow(_G, _length, const1map, _s, _t) { }
98
99    ///Runs the algorithm.
100
101    ///Runs the algorithm.
102    ///Returns k if there are at least k edge-disjoint paths from s to t.
103    ///Otherwise it returns the number of edge-disjoint paths found
104    ///from s to t.
105    ///
106    ///\param k How many paths are we looking for?
107    ///
108    int run(int k) {
109      int i = min_cost_flow.run(k);
110
111      //Let's find the paths
112      //We put the paths into stl vectors (as an inner representation).
113      //In the meantime we lose the information stored in 'reversed'.
114      //We suppose the lengths to be positive now.
115
116      //We don't want to change the flow of min_cost_flow, so we make a copy
117      //The name here suggests that the flow has only 0/1 values.
118      EdgeIntMap reversed(G);
119
120      for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
121        reversed[e] = min_cost_flow.getFlow()[e];
122     
123      paths.clear();
124      paths.resize(k);
125      for (int j=0; j<i; ++j){
126        Node n=s;
127
128        while (n!=t){
129
130          OutEdgeIt e(G, n);
131         
132          while (!reversed[e]){
133            ++e;
134          }
135          n = G.target(e);
136          paths[j].push_back(e);
137          reversed[e] = 1-reversed[e];
138        }
139       
140      }
141      return i;
142    }
143
144   
145    ///Returns the total length of the paths.
146   
147    ///This function gives back the total length of the found paths.
148    Length totalLength(){
149      return min_cost_flow.totalLength();
150    }
151
152    ///Returns the found flow.
153
154    ///This function returns a const reference to the EdgeMap \c flow.
155    const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
156
157    /// Returns the optimal dual solution
158   
159    ///This function returns a const reference to the NodeMap
160    ///\c potential (the dual solution).
161    const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
162
163    ///Checks whether the complementary slackness holds.
164
165    ///This function checks, whether the given solution is optimal.
166    ///Currently this function only checks optimality,
167    ///doesn't bother with feasibility.
168    ///It is meant for testing purposes.
169    bool checkComplementarySlackness(){
170      return min_cost_flow.checkComplementarySlackness();
171    }
172
173    ///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 since then.
177    /// \warning It is assumed that \c p is constructed to
178    ///be a path of graph \c G.
179    ///If \c j is not less than the result of previous \c run,
180    ///then the result here will be an empty path (\c j can be 0 as well).
181    ///
182    ///\param Path The type of the path structure to put the result to (must meet lemon path concept).
183    ///\param p The path to put the result to.
184    ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively).
185    template<typename Path>
186    void getPath(Path& p, size_t j){
187
188      p.clear();
189      if (j>paths.size()-1){
190        return;
191      }
192      typename Path::Builder B(p);
193      for(typename std::vector<Edge>::iterator i=paths[j].begin();
194          i!=paths[j].end(); ++i ){
195        B.pushBack(*i);
196      }
197
198      B.commit();
199    }
200
201  }; //class Suurballe
202
203  ///@}
204
205} //namespace lemon
206
207#endif //LEMON_SUURBALLE_H
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