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
2.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
2.2 +++ b/src/hugo/minlengthpaths.h Tue May 11 16:15:18 2004 +0000
2.3 @@ -0,0 +1,164 @@
2.4 +// -*- c++ -*-
2.5 +#ifndef HUGO_MINLENGTHPATHS_H
2.6 +#define HUGO_MINLENGTHPATHS_H
2.7 +
2.8 +///\ingroup galgs
2.9 +///\file
2.10 +///\brief An algorithm for finding k paths of minimal total length.
2.11 +
2.12 +#include <iostream>
2.13 +//#include <hugo/dijkstra.h>
2.14 +//#include <hugo/graph_wrapper.h>
2.15 +#include <hugo/maps.h>
2.16 +#include <vector>
2.17 +#include <hugo/mincostflows.h>
2.18 +#include <for_each_macros.h>
2.19 +
2.20 +namespace hugo {
2.21 +
2.22 +/// \addtogroup galgs
2.23 +/// @{
2.24 +
2.25 + ///\brief Implementation of an algorithm for finding k paths between 2 nodes
2.26 + /// of minimal total length
2.27 + ///
2.28 + /// The class \ref hugo::MinLengthPaths "MinLengthPaths" implements
2.29 + /// an algorithm for finding k edge-disjoint paths
2.30 + /// from a given source node to a given target node in an
2.31 + /// edge-weighted directed graph having minimal total weigth (length).
2.32 + ///
2.33 + ///\warning It is assumed that the lengths are positive, since the
2.34 + /// general flow-decomposition is not implemented yet.
2.35 + ///
2.36 + ///\author Attila Bernath
2.37 + template <typename Graph, typename LengthMap>
2.38 + class MinLengthPaths{
2.39 +
2.40 +
2.41 + typedef typename LengthMap::ValueType Length;
2.42 +
2.43 + typedef typename Graph::Node Node;
2.44 + typedef typename Graph::NodeIt NodeIt;
2.45 + typedef typename Graph::Edge Edge;
2.46 + typedef typename Graph::OutEdgeIt OutEdgeIt;
2.47 + typedef typename Graph::template EdgeMap<int> EdgeIntMap;
2.48 +
2.49 + typedef ConstMap<Edge,int> ConstMap;
2.50 +
2.51 + //Input
2.52 + const Graph& G;
2.53 +
2.54 + //Auxiliary variables
2.55 + //This is the capacity map for the mincostflow problem
2.56 + ConstMap const1map;
2.57 + //This MinCostFlows instance will actually solve the problem
2.58 + MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow;
2.59 +
2.60 + //Container to store found paths
2.61 + std::vector< std::vector<Edge> > paths;
2.62 +
2.63 + public :
2.64 +
2.65 +
2.66 + MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G),
2.67 + const1map(1), mincost_flow(_G, _length, const1map){}
2.68 +
2.69 + ///Runs the algorithm.
2.70 +
2.71 + ///Runs the algorithm.
2.72 + ///Returns k if there are at least k edge-disjoint paths from s to t.
2.73 + ///Otherwise it returns the number of found edge-disjoint paths from s to t.
2.74 + int run(Node s, Node t, int k) {
2.75 +
2.76 + int i = mincost_flow.run(s,t,k);
2.77 +
2.78 +
2.79 +
2.80 + //Let's find the paths
2.81 + //We put the paths into stl vectors (as an inner representation).
2.82 + //In the meantime we lose the information stored in 'reversed'.
2.83 + //We suppose the lengths to be positive now.
2.84 +
2.85 + //We don't want to change the flow of mincost_flow, so we make a copy
2.86 + //The name here suggests that the flow has only 0/1 values.
2.87 + EdgeIntMap reversed(G);
2.88 +
2.89 + FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
2.90 + reversed[e] = mincost_flow.getFlow()[e];
2.91 + }
2.92 +
2.93 + paths.clear();
2.94 + //total_length=0;
2.95 + paths.resize(k);
2.96 + for (int j=0; j<i; ++j){
2.97 + Node n=s;
2.98 + OutEdgeIt e;
2.99 +
2.100 + while (n!=t){
2.101 +
2.102 +
2.103 + G.first(e,n);
2.104 +
2.105 + while (!reversed[e]){
2.106 + G.next(e);
2.107 + }
2.108 + n = G.head(e);
2.109 + paths[j].push_back(e);
2.110 + //total_length += length[e];
2.111 + reversed[e] = 1-reversed[e];
2.112 + }
2.113 +
2.114 + }
2.115 + return i;
2.116 + }
2.117 +
2.118 +
2.119 + ///This function gives back the total length of the found paths.
2.120 + ///Assumes that \c run() has been run and nothing changed since then.
2.121 + Length totalLength(){
2.122 + return mincost_flow.totalLength();
2.123 + }
2.124 +
2.125 + ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
2.126 + ///be called before using this function.
2.127 + const EdgeIntMap &getFlow() const { return mincost_flow.flow;}
2.128 +
2.129 + ///Returns a const reference to the NodeMap \c potential (the dual solution).
2.130 + /// \pre \ref run() must be called before using this function.
2.131 + const EdgeIntMap &getPotential() const { return mincost_flow.potential;}
2.132 +
2.133 + ///This function checks, whether the given solution is optimal
2.134 + ///Running after a \c run() should return with true
2.135 + ///In this "state of the art" this only checks optimality, doesn't bother with feasibility
2.136 + ///
2.137 + ///\todo Is this OK here?
2.138 + bool checkComplementarySlackness(){
2.139 + return mincost_flow.checkComplementarySlackness();
2.140 + }
2.141 +
2.142 + ///This function gives back the \c j-th path in argument p.
2.143 + ///Assumes that \c run() has been run and nothing changed since then.
2.144 + /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is not less than the result of previous \c run, then the result here will be an empty path (\c j can be 0 as well).
2.145 + template<typename DirPath>
2.146 + void getPath(DirPath& p, size_t j){
2.147 +
2.148 + p.clear();
2.149 + if (j>paths.size()-1){
2.150 + return;
2.151 + }
2.152 + typename DirPath::Builder B(p);
2.153 + for(typename std::vector<Edge>::iterator i=paths[j].begin();
2.154 + i!=paths[j].end(); ++i ){
2.155 + B.pushBack(*i);
2.156 + }
2.157 +
2.158 + B.commit();
2.159 + }
2.160 +
2.161 + }; //class MinLengthPaths
2.162 +
2.163 + ///@}
2.164 +
2.165 +} //namespace hugo
2.166 +
2.167 +#endif //HUGO_MINLENGTHPATHS_H
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/src/test/minlengthpaths_test.cc Tue May 11 16:15:18 2004 +0000
3.3 @@ -0,0 +1,99 @@
3.4 +#include <iostream>
3.5 +#include <hugo/list_graph.h>
3.6 +#include <hugo/minlengthpaths.h>
3.7 +#include <path.h>
3.8 +
3.9 +using namespace std;
3.10 +using namespace hugo;
3.11 +
3.12 +
3.13 +
3.14 +bool passed = true;
3.15 +
3.16 +void check(bool rc, char *msg="") {
3.17 + passed = passed && rc;
3.18 + if(!rc) {
3.19 + std::cerr << "Test failed! ("<< msg << ")" << std::endl; \
3.20 +
3.21 +
3.22 + }
3.23 +}
3.24 +
3.25 +
3.26 +
3.27 +int main()
3.28 +{
3.29 +
3.30 + typedef ListGraph::Node Node;
3.31 + typedef ListGraph::Edge Edge;
3.32 +
3.33 + ListGraph graph;
3.34 +
3.35 + //Ahuja könyv példája
3.36 +
3.37 + Node s=graph.addNode();
3.38 + Node v1=graph.addNode();
3.39 + Node v2=graph.addNode();
3.40 + Node v3=graph.addNode();
3.41 + Node v4=graph.addNode();
3.42 + Node v5=graph.addNode();
3.43 + Node t=graph.addNode();
3.44 +
3.45 + Edge s_v1=graph.addEdge(s, v1);
3.46 + Edge v1_v2=graph.addEdge(v1, v2);
3.47 + Edge s_v3=graph.addEdge(s, v3);
3.48 + Edge v2_v4=graph.addEdge(v2, v4);
3.49 + Edge v2_v5=graph.addEdge(v2, v5);
3.50 + Edge v3_v5=graph.addEdge(v3, v5);
3.51 + Edge v4_t=graph.addEdge(v4, t);
3.52 + Edge v5_t=graph.addEdge(v5, t);
3.53 +
3.54 +
3.55 + ListGraph::EdgeMap<int> length(graph);
3.56 +
3.57 + length.set(s_v1, 6);
3.58 + length.set(v1_v2, 4);
3.59 + length.set(s_v3, 10);
3.60 + length.set(v2_v4, 5);
3.61 + length.set(v2_v5, 1);
3.62 + length.set(v3_v5, 5);
3.63 + length.set(v4_t, 8);
3.64 + length.set(v5_t, 8);
3.65 +
3.66 + std::cout << "Minlengthpaths algorithm test..." << std::endl;
3.67 +
3.68 +
3.69 + int k=3;
3.70 + MinLengthPaths< ListGraph, ListGraph::EdgeMap<int> >
3.71 + surb_test(graph, length);
3.72 +
3.73 + check( surb_test.run(s,t,k) == 2 && surb_test.totalLength() == 46,"Two paths, total length should be 46");
3.74 +
3.75 + check( surb_test.checkComplementarySlackness(), "Complementary slackness conditions are not met.");
3.76 +
3.77 + typedef DirPath<ListGraph> DPath;
3.78 + DPath P(graph);
3.79 +
3.80 + /*
3.81 + surb_test.getPath(P,0);
3.82 + check(P.length() == 4, "First path should contain 4 edges.");
3.83 + cout<<P.length()<<endl;
3.84 + surb_test.getPath(P,1);
3.85 + check(P.length() == 3, "Second path: 3 edges.");
3.86 + cout<<P.length()<<endl;
3.87 + */
3.88 +
3.89 + k=1;
3.90 + check( surb_test.run(s,t,k) == 1 && surb_test.totalLength() == 19,"One path, total length should be 19");
3.91 +
3.92 + check( surb_test.checkComplementarySlackness(), "Complementary slackness conditions are not met.");
3.93 +
3.94 + surb_test.getPath(P,0);
3.95 + check(P.length() == 4, "First path should contain 4 edges.");
3.96 +
3.97 + cout << (passed ? "All tests passed." : "Some of the tests failed!!!")
3.98 + << endl;
3.99 +
3.100 + return passed ? 0 : 1;
3.101 +
3.102 +}