COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/mincostflows.h @ 638:2153dd45937a

Last change on this file since 638:2153dd45937a was 634:aacabcd724f0, checked in by athos, 17 years ago

Another slight modifications.

File size: 6.0 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
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
96    Length total_length;
97
98
99  public :
100
101
102    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
103      length(_length), capacity(_cap), flow(_G), potential(_G){ }
104
105   
106    ///Runs the algorithm.
107
108    ///Runs the algorithm.
109    ///Returns k if there are at least k edge-disjoint paths from s to t.
110    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
111    ///\todo May be it does make sense to be able to start with a nonzero
112    /// feasible primal-dual solution pair as well.
113    int run(Node s, Node t, int k) {
114
115      //Resetting variables from previous runs
116      total_length = 0;
117     
118      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
119        flow.set(e,0);
120      }
121
122      //Initialize the potential to zero
123      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
124        potential.set(n,0);
125      }
126     
127
128     
129      //We need a residual graph
130      ResGraphType res_graph(G, capacity, flow);
131
132
133      ModLengthMap mod_length(res_graph, length, potential);
134
135      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
136
137      int i;
138      for (i=0; i<k; ++i){
139        dijkstra.run(s);
140        if (!dijkstra.reached(t)){
141          //There are no k paths from s to t
142          break;
143        };
144       
145        //We have to change the potential
146        FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){
147          potential[n] += dijkstra.distMap()[n];
148        }
149
150
151        //Augmenting on the sortest path
152        Node n=t;
153        ResGraphEdge e;
154        while (n!=s){
155          e = dijkstra.pred(n);
156          n = dijkstra.predNode(n);
157          res_graph.augment(e,1);
158          //Let's update the total length
159          if (res_graph.forward(e))
160            total_length += length[e];
161          else
162            total_length -= length[e];     
163        }
164
165         
166      }
167     
168
169      return i;
170    }
171
172
173
174
175    ///This function gives back the total length of the found paths.
176    ///Assumes that \c run() has been run and nothing changed since then.
177    Length totalLength(){
178      return total_length;
179    }
180
181    ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
182    ///be called before using this function.
183    const EdgeIntMap &getFlow() const { return flow;}
184
185  ///Returns a const reference to the NodeMap \c potential (the dual solution).
186    /// \pre \ref run() must be called before using this function.
187    const EdgeIntMap &getPotential() const { return potential;}
188
189    ///This function checks, whether the given solution is optimal
190    ///Running after a \c run() should return with true
191    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
192    ///
193    ///\todo Is this OK here?
194    bool checkComplementarySlackness(){
195      Length mod_pot;
196      Length fl_e;
197      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
198        //C^{\Pi}_{i,j}
199        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
200        fl_e = flow[e];
201        //      std::cout << fl_e << std::endl;
202        if (0<fl_e && fl_e<capacity[e]){
203          if (mod_pot != 0)
204            return false;
205        }
206        else{
207          if (mod_pot > 0 && fl_e != 0)
208            return false;
209          if (mod_pot < 0 && fl_e != capacity[e])
210            return false;
211        }
212      }
213      return true;
214    }
215   
216
217  }; //class MinCostFlows
218
219  ///@}
220
221} //namespace hugo
222
223#endif //HUGO_MINCOSTFLOWS_H
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