COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/minlengthpaths.h @ 860:3577b3db6089

Last change on this file since 860:3577b3db6089 was 860:3577b3db6089, checked in by athos, 17 years ago

Completed documentation for mincostflows and minlengthpaths.

File size: 5.4 KB
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1// -*- c++ -*-
2#ifndef HUGO_MINLENGTHPATHS_H
3#define HUGO_MINLENGTHPATHS_H
4
5///\ingroup flowalgs
6///\file
7///\brief An algorithm for finding k paths of minimal total length.
8
9
10#include <hugo/maps.h>
11#include <vector>
12#include <hugo/mincostflows.h>
13
14namespace hugo {
15
16/// \addtogroup flowalgs
17/// @{
18
19  ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes
20  /// of minimal total length
21  ///
22  /// The class \ref hugo::MinLengthPaths implements
23  /// an algorithm for finding k edge-disjoint paths
24  /// from a given source node to a given target node in an
25  /// edge-weighted directed graph having minimal total weight (length).
26  ///
27  ///\warning Length values should be nonnegative.
28  ///
29  ///\param Graph The directed graph type the algorithm runs on.
30  ///\param LengthMap The type of the length map (values should be nonnegative).
31  ///
32  ///\author Attila Bernath
33  template <typename Graph, typename LengthMap>
34  class MinLengthPaths{
35
36
37    typedef typename LengthMap::ValueType Length;
38   
39    typedef typename Graph::Node Node;
40    typedef typename Graph::NodeIt NodeIt;
41    typedef typename Graph::Edge Edge;
42    typedef typename Graph::OutEdgeIt OutEdgeIt;
43    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
44
45    typedef ConstMap<Edge,int> ConstMap;
46
47    //Input
48    const Graph& G;
49
50    //Auxiliary variables
51    //This is the capacity map for the mincostflow problem
52    ConstMap const1map;
53    //This MinCostFlows instance will actually solve the problem
54    MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow;
55
56    //Container to store found paths
57    std::vector< std::vector<Edge> > paths;
58
59  public :
60
61
62    /// The constructor of the class.
63   
64    ///\param _G The directed graph the algorithm runs on.
65    ///\param _length The length (weight or cost) of the edges.
66    MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G),
67      const1map(1), mincost_flow(_G, _length, const1map){}
68
69    ///Runs the algorithm.
70
71    ///Runs the algorithm.
72    ///Returns k if there are at least k edge-disjoint paths from s to t.
73    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
74    ///
75    ///\param s The source node.
76    ///\param t The target node.
77    ///\param k How many paths are we looking for?
78    ///
79    int run(Node s, Node t, int k) {
80
81      int i = mincost_flow.run(s,t,k);
82   
83
84      //Let's find the paths
85      //We put the paths into stl vectors (as an inner representation).
86      //In the meantime we lose the information stored in 'reversed'.
87      //We suppose the lengths to be positive now.
88
89      //We don't want to change the flow of mincost_flow, so we make a copy
90      //The name here suggests that the flow has only 0/1 values.
91      EdgeIntMap reversed(G);
92
93      for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
94        reversed[e] = mincost_flow.getFlow()[e];
95     
96      paths.clear();
97      //total_length=0;
98      paths.resize(k);
99      for (int j=0; j<i; ++j){
100        Node n=s;
101        OutEdgeIt e;
102
103        while (n!=t){
104
105
106          G.first(e,n);
107         
108          while (!reversed[e]){
109            ++e;
110          }
111          n = G.head(e);
112          paths[j].push_back(e);
113          //total_length += length[e];
114          reversed[e] = 1-reversed[e];
115        }
116       
117      }
118      return i;
119    }
120
121   
122    ///Returns the total length of the paths
123   
124    ///This function gives back the total length of the found paths.
125    ///\pre \ref run() must
126    ///be called before using this function.
127    Length totalLength(){
128      return mincost_flow.totalLength();
129    }
130
131    ///Returns the found flow.
132
133    ///This function returns a const reference to the EdgeMap \c flow.
134    ///\pre \ref run() must
135    ///be called before using this function.
136    const EdgeIntMap &getFlow() const { return mincost_flow.flow;}
137
138    /// Returns the optimal dual solution
139   
140    ///This function returns a const reference to the NodeMap
141    ///\c potential (the dual solution).
142    /// \pre \ref run() must be called before using this function.
143    const EdgeIntMap &getPotential() const { return mincost_flow.potential;}
144
145    ///Checks whether the complementary slackness holds.
146
147    ///This function checks, whether the given solution is optimal.
148    ///It should return true after calling \ref run()
149    ///Currently this function only checks optimality,
150    ///doesn't bother with feasibility
151    ///It is meant for testing purposes.
152    ///
153    bool checkComplementarySlackness(){
154      return mincost_flow.checkComplementarySlackness();
155    }
156
157    ///Read the found paths.
158   
159    ///This function gives back the \c j-th path in argument p.
160    ///Assumes that \c run() has been run and nothing changed since then.
161    /// \warning It is assumed that \c p is constructed to
162    ///be a path of graph \c G.
163    ///If \c j is not less than the result of previous \c run,
164    ///then the result here will be an empty path (\c j can be 0 as well).
165    ///
166    ///\param Path The type of the path structure to put the result to (must meet hugo path concept).
167    ///\param p The path to put the result to
168    ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
169    template<typename Path>
170    void getPath(Path& p, size_t j){
171
172      p.clear();
173      if (j>paths.size()-1){
174        return;
175      }
176      typename Path::Builder B(p);
177      for(typename std::vector<Edge>::iterator i=paths[j].begin();
178          i!=paths[j].end(); ++i ){
179        B.pushBack(*i);
180      }
181
182      B.commit();
183    }
184
185  }; //class MinLengthPaths
186
187  ///@}
188
189} //namespace hugo
190
191#endif //HUGO_MINLENGTHPATHS_H
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