COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/lemon/suurballe.h @ 943:cb0ac054ea92

Last change on this file since 943:cb0ac054ea92 was 941:186aa53d2802, checked in by marci, 16 years ago

Suurballe and MinCostFlow? classes are now able to increase the flow 1 by 1 with
this->augment()

File size: 6.3 KB
Line 
1/* -*- C++ -*-
2 * src/lemon/suurballe.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Combinatorial Optimization Research Group, 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 if it is correct to call this method after
48  ///%Suurballe for it is just a special case of Edmond's and Karp's algorithm
49  ///for finding minimum cost flows. In fact, this implementation is 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::ValueType 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      //total_length=0;
125      paths.resize(k);
126      for (int j=0; j<i; ++j){
127        Node n=s;
128        OutEdgeIt e;
129
130        while (n!=t){
131
132
133          G.first(e,n);
134         
135          while (!reversed[e]){
136            ++e;
137          }
138          n = G.head(e);
139          paths[j].push_back(e);
140          //total_length += length[e];
141          reversed[e] = 1-reversed[e];
142        }
143       
144      }
145      return i;
146    }
147
148   
149    ///Returns the total length of the paths.
150   
151    ///This function gives back the total length of the found paths.
152    Length totalLength(){
153      return min_cost_flow.totalLength();
154    }
155
156    ///Returns the found flow.
157
158    ///This function returns a const reference to the EdgeMap \c flow.
159    const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
160
161    /// Returns the optimal dual solution
162   
163    ///This function returns a const reference to the NodeMap
164    ///\c potential (the dual solution).
165    const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
166
167    ///Checks whether the complementary slackness holds.
168
169    ///This function checks, whether the given solution is optimal.
170    ///Currently this function only checks optimality,
171    ///doesn't bother with feasibility
172    ///It is meant for testing purposes.
173    bool checkComplementarySlackness(){
174      return min_cost_flow.checkComplementarySlackness();
175    }
176
177    ///Read the found paths.
178   
179    ///This function gives back the \c j-th path in argument p.
180    ///Assumes that \c run() has been run and nothing changed since then.
181    /// \warning It is assumed that \c p is constructed to
182    ///be a path of graph \c G.
183    ///If \c j is not less than the result of previous \c run,
184    ///then the result here will be an empty path (\c j can be 0 as well).
185    ///
186    ///\param Path The type of the path structure to put the result to (must meet lemon path concept).
187    ///\param p The path to put the result to
188    ///\param j Which path you want to get from the found paths (in a 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
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