COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/mincostflows.h @ 547:50184b822370

Last change on this file since 547:50184b822370 was 547:50184b822370, checked in by athos, 16 years ago

Modified a little bit

File size: 5.8 KB
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1// -*- c++ -*-
2#ifndef HUGO_MINCOSTFLOWS_H
3#define HUGO_MINCOSTFLOWS_H
4
5///\ingroup galgs
6///\file
7///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost
8
9#include <iostream>
10#include <dijkstra.h>
11#include <graph_wrapper.h>
12#include <maps.h>
13#include <vector.h>
14#include <for_each_macros.h>
15
16namespace hugo {
17
18/// \addtogroup galgs
19/// @{
20
21  ///\brief Implementation of an algorithm for finding a flow of value \c k
22  ///(for small values of \c k) having minimal total cost between 2 nodes
23  ///
24  ///
25  /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
26  /// an algorithm for finding a flow of value \c k
27  ///(for small values of \c k) having minimal total cost 
28  /// from a given source node to a given target node in an
29  /// edge-weighted directed graph having nonnegative integer capacities.
30  /// The range of the length (weight) function is nonnegative reals but
31  /// the range of capacity function is the set of nonnegative integers.
32  /// It is not a polinomial time algorithm for counting the minimum cost
33  /// maximal flow, since it counts the minimum cost flow for every value 0..M
34  /// where \c M is the value of the maximal flow.
35  ///
36  ///\author Attila Bernath
37  template <typename Graph, typename LengthMap, typename CapacityMap>
38  class MinCostFlows {
39
40    typedef typename LengthMap::ValueType Length;
41
42    //Warning: this should be integer type
43    typedef typename CapacityMap::ValueType Capacity;
44   
45    typedef typename Graph::Node Node;
46    typedef typename Graph::NodeIt NodeIt;
47    typedef typename Graph::Edge Edge;
48    typedef typename Graph::OutEdgeIt OutEdgeIt;
49    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
50
51    //    typedef ConstMap<Edge,int> ConstMap;
52
53    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
54    typedef typename ResGraphType::Edge ResGraphEdge;
55
56    class ModLengthMap {   
57      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
58      typedef typename Graph::template NodeMap<Length> NodeMap;
59      const ResGraphType& G;
60      //      const EdgeIntMap& rev;
61      const LengthMap &ol;
62      const NodeMap &pot;
63    public :
64      typedef typename LengthMap::KeyType KeyType;
65      typedef typename LengthMap::ValueType ValueType;
66       
67      ValueType operator[](typename ResGraphType::Edge e) const {     
68        if (G.forward(e))
69          return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
70        else
71          return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
72      }     
73       
74      ModLengthMap(const ResGraphType& _G,
75                   const LengthMap &o,  const NodeMap &p) :
76        G(_G), /*rev(_rev),*/ ol(o), pot(p){};
77    };//ModLengthMap
78
79
80   
81    //Input
82    const Graph& G;
83    const LengthMap& length;
84    const CapacityMap& capacity;
85
86    //auxiliary variables
87
88    //The value is 1 iff the edge is reversed.
89    //If the algorithm has finished, the edges of the seeked paths are
90    //exactly those that are reversed
91    EdgeIntMap flow;
92    typename Graph::template NodeMap<Length> potential;
93   
94    //Container to store found paths
95    std::vector< std::vector<Edge> > paths;
96    //typedef DirPath<Graph> DPath;
97    //DPath paths;
98
99
100    Length total_length;
101
102  public :
103
104
105    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
106      length(_length), capacity(_cap), flow(_G), potential(_G){ }
107
108   
109    ///Runs the algorithm.
110
111    ///Runs the algorithm.
112    ///Returns k if there are at least k edge-disjoint paths from s to t.
113    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
114    int run(Node s, Node t, int k) {
115
116      //Resetting variables from previous runs
117      total_length = 0;
118     
119      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
120        flow.set(e,0);
121      }
122     
123      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
124        //cout << potential[n]<<endl;
125        potential.set(n,0);
126      }
127     
128
129     
130      //We need a residual graph
131      ResGraphType res_graph(G, capacity, flow);
132
133      //Initialize the copy of the Dijkstra potential to zero
134     
135      //typename ResGraphType::template NodeMap<Length> potential(res_graph);
136
137
138      ModLengthMap mod_length(res_graph, length, potential);
139
140      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
141
142      int i;
143      for (i=0; i<k; ++i){
144        dijkstra.run(s);
145        if (!dijkstra.reached(t)){
146          //There are no k paths from s to t
147          break;
148        };
149       
150        {
151          //We have to copy the potential
152          typename ResGraphType::NodeIt n;
153          for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
154              potential[n] += dijkstra.distMap()[n];
155          }
156        }
157
158
159        //Augmenting on the sortest path
160        Node n=t;
161        ResGraphEdge e;
162        while (n!=s){
163          e = dijkstra.pred(n);
164          n = dijkstra.predNode(n);
165          res_graph.augment(e,1);
166          //Let's update the total length
167          if (res_graph.forward(e))
168            total_length += length[e];
169          else
170            total_length -= length[e];     
171        }
172
173         
174      }
175     
176
177      return i;
178    }
179
180
181
182
183    ///This function gives back the total length of the found paths.
184    ///Assumes that \c run() has been run and nothing changed since then.
185    Length totalLength(){
186      return total_length;
187    }
188
189    /*
190      ///\todo To be implemented later
191
192    ///This function gives back the \c j-th path in argument p.
193    ///Assumes that \c run() has been run and nothing changed since then.
194    /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path.
195    template<typename DirPath>
196    void getPath(DirPath& p, int j){
197      p.clear();
198      typename DirPath::Builder B(p);
199      for(typename std::vector<Edge>::iterator i=paths[j].begin();
200          i!=paths[j].end(); ++i ){
201        B.pushBack(*i);
202      }
203
204      B.commit();
205    }
206
207    */
208
209  }; //class MinCostFlows
210
211  ///@}
212
213} //namespace hugo
214
215#endif //HUGO_MINCOSTFLOW_H
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