COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/mincostflows.h @ 527:7550fed0cd91

Last change on this file since 527:7550fed0cd91 was 527:7550fed0cd91, checked in by athos, 16 years ago

Nem tudom, a hugo-n miert nem megy.

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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
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>
38  class MinCostFlows {
39
40    typedef typename LengthMap::ValueType Length;
41
42    typedef typename LengthMap::ValueType Length;
43   
44    typedef typename Graph::Node Node;
45    typedef typename Graph::NodeIt NodeIt;
46    typedef typename Graph::Edge Edge;
47    typedef typename Graph::OutEdgeIt OutEdgeIt;
48    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
49
50    //    typedef ConstMap<Edge,int> ConstMap;
51
52    typedef ResGraphWrapper<const Graph,int,EdgeIntMap,EdgeIntMap> ResGraphType;
53
54    class ModLengthMap {   
55      typedef typename ResGraphType::template NodeMap<Length> NodeMap;
56      const ResGraphType& G;
57      //      const EdgeIntMap& rev;
58      const LengthMap &ol;
59      const NodeMap &pot;
60    public :
61      typedef typename LengthMap::KeyType KeyType;
62      typedef typename LengthMap::ValueType ValueType;
63       
64      ValueType operator[](typename ResGraphType::Edge e) const {     
65        if (G.forward(e))
66          return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
67        else
68          return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
69      }     
70       
71      ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev,
72                   const LengthMap &o,  const NodeMap &p) :
73        G(_G), /*rev(_rev),*/ ol(o), pot(p){};
74    };//ModLengthMap
75
76
77   
78    //Input
79    const Graph& G;
80    const LengthMap& length;
81    const EdgeIntMap& capacity;
82
83    //auxiliary variables
84
85    //The value is 1 iff the edge is reversed.
86    //If the algorithm has finished, the edges of the seeked paths are
87    //exactly those that are reversed
88    EdgeIntMap flow;
89   
90    //Container to store found paths
91    std::vector< std::vector<Edge> > paths;
92    //typedef DirPath<Graph> DPath;
93    //DPath paths;
94
95
96    Length total_length;
97
98  public :
99
100
101    MinLengthPaths(Graph& _G, LengthMap& _length, EdgeIntMap& _cap) : G(_G),
102      length(_length), capacity(_cap), flow(_G)/*, dijkstra_dist(_G)*/{ }
103
104   
105    ///Runs the algorithm.
106
107    ///Runs the algorithm.
108    ///Returns k if there are at least k edge-disjoint paths from s to t.
109    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
110    int run(Node s, Node t, int k) {
111
112
113      //We need a residual graph
114      ResGraphType res_graph(G, capacity, flow);
115
116      //Initialize the copy of the Dijkstra potential to zero
117      typename ResGraphType::template NodeMap<Length> dijkstra_dist(res_graph);
118      ModLengthMap mod_length(res_graph, length, dijkstra_dist);
119
120      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
121
122      int i;
123      for (i=0; i<k; ++i){
124        dijkstra.run(s);
125        if (!dijkstra.reached(t)){
126          //There are no k paths from s to t
127          break;
128        };
129       
130        {
131          //We have to copy the potential
132          typename ResGraphType::NodeIt n;
133          for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
134              dijkstra_dist[n] += dijkstra.distMap()[n];
135          }
136        }
137
138
139        //Augmenting on the sortest path
140        Node n=t;
141        Edge e;
142        while (n!=s){
143          e = dijkstra.pred(n);
144          n = dijkstra.predNode(n);
145          G.augment(e,1);
146        }
147
148         
149      }
150     
151      /*
152        ///\TODO To be implemented later
153
154      //Let's find the paths
155      //We put the paths into stl vectors (as an inner representation).
156      //In the meantime we lose the information stored in 'reversed'.
157      //We suppose the lengths to be positive now.
158
159      //Meanwhile we put the total length of the found paths
160      //in the member variable total_length
161      paths.clear();
162      total_length=0;
163      paths.resize(k);
164      for (int j=0; j<i; ++j){
165        Node n=s;
166        OutEdgeIt e;
167
168        while (n!=t){
169
170
171          G.first(e,n);
172         
173          while (!reversed[e]){
174            G.next(e);
175          }
176          n = G.head(e);
177          paths[j].push_back(e);
178          total_length += length[e];
179          reversed[e] = 1-reversed[e];
180        }
181       
182      }
183      */
184
185      return i;
186    }
187
188    ///This function gives back the total length of the found paths.
189    ///Assumes that \c run() has been run and nothing changed since then.
190    Length totalLength(){
191      return total_length;
192    }
193
194    ///This function gives back the \c j-th path in argument p.
195    ///Assumes that \c run() has been run and nothing changed since then.
196    /// \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.
197    template<typename DirPath>
198    void getPath(DirPath& p, int j){
199      p.clear();
200      typename DirPath::Builder B(p);
201      for(typename std::vector<Edge>::iterator i=paths[j].begin();
202          i!=paths[j].end(); ++i ){
203        B.pushBack(*i);
204      }
205
206      B.commit();
207    }
208
209  }; //class MinLengthPaths
210
211  ///@}
212
213} //namespace hugo
214
215#endif //HUGO_MINCOSTFLOW_H
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