1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/hugo/mincostflows.h Tue May 11 16:15:18 2004 +0000
1.3 @@ -0,0 +1,254 @@
1.4 +// -*- c++ -*-
1.5 +#ifndef HUGO_MINCOSTFLOWS_H
1.6 +#define HUGO_MINCOSTFLOWS_H
1.7 +
1.8 +///\ingroup galgs
1.9 +///\file
1.10 +///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost
1.11 +
1.12 +#include <iostream>
1.13 +#include <hugo/dijkstra.h>
1.14 +#include <hugo/graph_wrapper.h>
1.15 +#include <hugo/maps.h>
1.16 +#include <vector>
1.17 +#include <for_each_macros.h>
1.18 +
1.19 +namespace hugo {
1.20 +
1.21 +/// \addtogroup galgs
1.22 +/// @{
1.23 +
1.24 + ///\brief Implementation of an algorithm for finding a flow of value \c k
1.25 + ///(for small values of \c k) having minimal total cost between 2 nodes
1.26 + ///
1.27 + ///
1.28 + /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
1.29 + /// an algorithm for finding a flow of value \c k
1.30 + ///(for small values of \c k) having minimal total cost
1.31 + /// from a given source node to a given target node in an
1.32 + /// edge-weighted directed graph having nonnegative integer capacities.
1.33 + /// The range of the length (weight) function is nonnegative reals but
1.34 + /// the range of capacity function is the set of nonnegative integers.
1.35 + /// It is not a polinomial time algorithm for counting the minimum cost
1.36 + /// maximal flow, since it counts the minimum cost flow for every value 0..M
1.37 + /// where \c M is the value of the maximal flow.
1.38 + ///
1.39 + ///\author Attila Bernath
1.40 + template <typename Graph, typename LengthMap, typename CapacityMap>
1.41 + class MinCostFlows {
1.42 +
1.43 + typedef typename LengthMap::ValueType Length;
1.44 +
1.45 + //Warning: this should be integer type
1.46 + typedef typename CapacityMap::ValueType Capacity;
1.47 +
1.48 + typedef typename Graph::Node Node;
1.49 + typedef typename Graph::NodeIt NodeIt;
1.50 + typedef typename Graph::Edge Edge;
1.51 + typedef typename Graph::OutEdgeIt OutEdgeIt;
1.52 + typedef typename Graph::template EdgeMap<int> EdgeIntMap;
1.53 +
1.54 + // typedef ConstMap<Edge,int> ConstMap;
1.55 +
1.56 + typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
1.57 + typedef typename ResGraphType::Edge ResGraphEdge;
1.58 +
1.59 + class ModLengthMap {
1.60 + //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
1.61 + typedef typename Graph::template NodeMap<Length> NodeMap;
1.62 + const ResGraphType& G;
1.63 + // const EdgeIntMap& rev;
1.64 + const LengthMap &ol;
1.65 + const NodeMap &pot;
1.66 + public :
1.67 + typedef typename LengthMap::KeyType KeyType;
1.68 + typedef typename LengthMap::ValueType ValueType;
1.69 +
1.70 + ValueType operator[](typename ResGraphType::Edge e) const {
1.71 + if (G.forward(e))
1.72 + return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);
1.73 + else
1.74 + return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);
1.75 + }
1.76 +
1.77 + ModLengthMap(const ResGraphType& _G,
1.78 + const LengthMap &o, const NodeMap &p) :
1.79 + G(_G), /*rev(_rev),*/ ol(o), pot(p){};
1.80 + };//ModLengthMap
1.81 +
1.82 +
1.83 + protected:
1.84 +
1.85 + //Input
1.86 + const Graph& G;
1.87 + const LengthMap& length;
1.88 + const CapacityMap& capacity;
1.89 +
1.90 +
1.91 + //auxiliary variables
1.92 +
1.93 + //To store the flow
1.94 + EdgeIntMap flow;
1.95 + //To store the potentila (dual variables)
1.96 + typename Graph::template NodeMap<Length> potential;
1.97 +
1.98 + //Container to store found paths
1.99 + //std::vector< std::vector<Edge> > paths;
1.100 + //typedef DirPath<Graph> DPath;
1.101 + //DPath paths;
1.102 +
1.103 +
1.104 + Length total_length;
1.105 +
1.106 +
1.107 + public :
1.108 +
1.109 +
1.110 + MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
1.111 + length(_length), capacity(_cap), flow(_G), potential(_G){ }
1.112 +
1.113 +
1.114 + ///Runs the algorithm.
1.115 +
1.116 + ///Runs the algorithm.
1.117 + ///Returns k if there are at least k edge-disjoint paths from s to t.
1.118 + ///Otherwise it returns the number of found edge-disjoint paths from s to t.
1.119 + ///\todo May be it does make sense to be able to start with a nonzero
1.120 + /// feasible primal-dual solution pair as well.
1.121 + int run(Node s, Node t, int k) {
1.122 +
1.123 + //Resetting variables from previous runs
1.124 + total_length = 0;
1.125 +
1.126 + FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
1.127 + flow.set(e,0);
1.128 + }
1.129 +
1.130 + FOR_EACH_LOC(typename Graph::NodeIt, n, G){
1.131 + //cout << potential[n]<<endl;
1.132 + potential.set(n,0);
1.133 + }
1.134 +
1.135 +
1.136 +
1.137 + //We need a residual graph
1.138 + ResGraphType res_graph(G, capacity, flow);
1.139 +
1.140 + //Initialize the copy of the Dijkstra potential to zero
1.141 +
1.142 + //typename ResGraphType::template NodeMap<Length> potential(res_graph);
1.143 +
1.144 +
1.145 + ModLengthMap mod_length(res_graph, length, potential);
1.146 +
1.147 + Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
1.148 +
1.149 + int i;
1.150 + for (i=0; i<k; ++i){
1.151 + dijkstra.run(s);
1.152 + if (!dijkstra.reached(t)){
1.153 + //There are no k paths from s to t
1.154 + break;
1.155 + };
1.156 +
1.157 + {
1.158 + //We have to copy the potential
1.159 + typename ResGraphType::NodeIt n;
1.160 + for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
1.161 + potential[n] += dijkstra.distMap()[n];
1.162 + }
1.163 + }
1.164 +
1.165 +
1.166 + //Augmenting on the sortest path
1.167 + Node n=t;
1.168 + ResGraphEdge e;
1.169 + while (n!=s){
1.170 + e = dijkstra.pred(n);
1.171 + n = dijkstra.predNode(n);
1.172 + res_graph.augment(e,1);
1.173 + //Let's update the total length
1.174 + if (res_graph.forward(e))
1.175 + total_length += length[e];
1.176 + else
1.177 + total_length -= length[e];
1.178 + }
1.179 +
1.180 +
1.181 + }
1.182 +
1.183 +
1.184 + return i;
1.185 + }
1.186 +
1.187 +
1.188 +
1.189 +
1.190 + ///This function gives back the total length of the found paths.
1.191 + ///Assumes that \c run() has been run and nothing changed since then.
1.192 + Length totalLength(){
1.193 + return total_length;
1.194 + }
1.195 +
1.196 + ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
1.197 + ///be called before using this function.
1.198 + const EdgeIntMap &getFlow() const { return flow;}
1.199 +
1.200 + ///Returns a const reference to the NodeMap \c potential (the dual solution).
1.201 + /// \pre \ref run() must be called before using this function.
1.202 + const EdgeIntMap &getPotential() const { return potential;}
1.203 +
1.204 + ///This function checks, whether the given solution is optimal
1.205 + ///Running after a \c run() should return with true
1.206 + ///In this "state of the art" this only check optimality, doesn't bother with feasibility
1.207 + ///
1.208 + ///\todo Is this OK here?
1.209 + bool checkComplementarySlackness(){
1.210 + Length mod_pot;
1.211 + Length fl_e;
1.212 + FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
1.213 + //C^{\Pi}_{i,j}
1.214 + mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
1.215 + fl_e = flow[e];
1.216 + // std::cout << fl_e << std::endl;
1.217 + if (0<fl_e && fl_e<capacity[e]){
1.218 + if (mod_pot != 0)
1.219 + return false;
1.220 + }
1.221 + else{
1.222 + if (mod_pot > 0 && fl_e != 0)
1.223 + return false;
1.224 + if (mod_pot < 0 && fl_e != capacity[e])
1.225 + return false;
1.226 + }
1.227 + }
1.228 + return true;
1.229 + }
1.230 +
1.231 + /*
1.232 + ///\todo To be implemented later
1.233 +
1.234 + ///This function gives back the \c j-th path in argument p.
1.235 + ///Assumes that \c run() has been run and nothing changed since then.
1.236 + /// \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.
1.237 + template<typename DirPath>
1.238 + void getPath(DirPath& p, int j){
1.239 + p.clear();
1.240 + typename DirPath::Builder B(p);
1.241 + for(typename std::vector<Edge>::iterator i=paths[j].begin();
1.242 + i!=paths[j].end(); ++i ){
1.243 + B.pushBack(*i);
1.244 + }
1.245 +
1.246 + B.commit();
1.247 + }
1.248 +
1.249 + */
1.250 +
1.251 + }; //class MinCostFlows
1.252 +
1.253 + ///@}
1.254 +
1.255 +} //namespace hugo
1.256 +
1.257 +#endif //HUGO_MINCOSTFLOW_H