COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/mincostflows.h @ 607:327f7cf13843

Last change on this file since 607:327f7cf13843 was 607:327f7cf13843, checked in by athos, 17 years ago

Finished MinLengthPaths?: a specialization of MinCostFlows?.

File size: 7.0 KB
Line 
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 <hugo/dijkstra.h>
11#include <hugo/graph_wrapper.h>
12#include <hugo/maps.h>
13#include <vector>
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  protected:
81   
82    //Input
83    const Graph& G;
84    const LengthMap& length;
85    const CapacityMap& capacity;
86
87
88    //auxiliary variables
89
90    //To store the flow
91    EdgeIntMap flow;
92    //To store the potentila (dual variables)
93    typename Graph::template NodeMap<Length> potential;
94   
95    //Container to store found paths
96    //std::vector< std::vector<Edge> > paths;
97    //typedef DirPath<Graph> DPath;
98    //DPath paths;
99
100
101    Length total_length;
102
103
104  public :
105
106
107    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
108      length(_length), capacity(_cap), flow(_G), potential(_G){ }
109
110   
111    ///Runs the algorithm.
112
113    ///Runs the algorithm.
114    ///Returns k if there are at least k edge-disjoint paths from s to t.
115    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
116    ///\todo May be it does make sense to be able to start with a nonzero
117    /// feasible primal-dual solution pair as well.
118    int run(Node s, Node t, int k) {
119
120      //Resetting variables from previous runs
121      total_length = 0;
122     
123      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
124        flow.set(e,0);
125      }
126     
127      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
128        //cout << potential[n]<<endl;
129        potential.set(n,0);
130      }
131     
132
133     
134      //We need a residual graph
135      ResGraphType res_graph(G, capacity, flow);
136
137      //Initialize the copy of the Dijkstra potential to zero
138     
139      //typename ResGraphType::template NodeMap<Length> potential(res_graph);
140
141
142      ModLengthMap mod_length(res_graph, length, potential);
143
144      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
145
146      int i;
147      for (i=0; i<k; ++i){
148        dijkstra.run(s);
149        if (!dijkstra.reached(t)){
150          //There are no k paths from s to t
151          break;
152        };
153       
154        {
155          //We have to copy the potential
156          typename ResGraphType::NodeIt n;
157          for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
158              potential[n] += dijkstra.distMap()[n];
159          }
160        }
161
162
163        //Augmenting on the sortest path
164        Node n=t;
165        ResGraphEdge e;
166        while (n!=s){
167          e = dijkstra.pred(n);
168          n = dijkstra.predNode(n);
169          res_graph.augment(e,1);
170          //Let's update the total length
171          if (res_graph.forward(e))
172            total_length += length[e];
173          else
174            total_length -= length[e];     
175        }
176
177         
178      }
179     
180
181      return i;
182    }
183
184
185
186
187    ///This function gives back the total length of the found paths.
188    ///Assumes that \c run() has been run and nothing changed since then.
189    Length totalLength(){
190      return total_length;
191    }
192
193    ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
194    ///be called before using this function.
195    const EdgeIntMap &getFlow() const { return flow;}
196
197  ///Returns a const reference to the NodeMap \c potential (the dual solution).
198    /// \pre \ref run() must be called before using this function.
199    const EdgeIntMap &getPotential() const { return potential;}
200
201    ///This function checks, whether the given solution is optimal
202    ///Running after a \c run() should return with true
203    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
204    ///
205    ///\todo Is this OK here?
206    bool checkComplementarySlackness(){
207      Length mod_pot;
208      Length fl_e;
209      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
210        //C^{\Pi}_{i,j}
211        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
212        fl_e = flow[e];
213        //      std::cout << fl_e << std::endl;
214        if (0<fl_e && fl_e<capacity[e]){
215          if (mod_pot != 0)
216            return false;
217        }
218        else{
219          if (mod_pot > 0 && fl_e != 0)
220            return false;
221          if (mod_pot < 0 && fl_e != capacity[e])
222            return false;
223        }
224      }
225      return true;
226    }
227   
228    /*
229      ///\todo To be implemented later
230
231    ///This function gives back the \c j-th path in argument p.
232    ///Assumes that \c run() has been run and nothing changed since then.
233    /// \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.
234    template<typename DirPath>
235    void getPath(DirPath& p, int j){
236      p.clear();
237      typename DirPath::Builder B(p);
238      for(typename std::vector<Edge>::iterator i=paths[j].begin();
239          i!=paths[j].end(); ++i ){
240        B.pushBack(*i);
241      }
242
243      B.commit();
244    }
245
246    */
247
248  }; //class MinCostFlows
249
250  ///@}
251
252} //namespace hugo
253
254#endif //HUGO_MINCOSTFLOW_H
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