1.1 --- a/src/work/athos/mincostflows.h Tue May 11 15:42:11 2004 +0000
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,254 +0,0 @@
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