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
2.1 --- a/src/work/athos/minlengthpaths.h Tue May 11 15:42:11 2004 +0000
2.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
2.3 @@ -1,164 +0,0 @@
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 <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 --- a/src/work/athos/minlengthpaths_test.cc Tue May 11 15:42:11 2004 +0000
3.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
3.3 @@ -1,96 +0,0 @@
3.4 -#include <iostream>
3.5 -#include <list_graph.h>
3.6 -#include <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 - surb_test.getPath(P,0);
3.81 - check(P.length() == 4, "First path should contain 4 edges.");
3.82 -
3.83 - surb_test.getPath(P,1);
3.84 - check(P.length() == 3, "Second path: 3 edges.");
3.85 -
3.86 - k=1;
3.87 - check( surb_test.run(s,t,k) == 1 && surb_test.totalLength() == 19,"One path, total length should be 19");
3.88 -
3.89 - check( surb_test.checkComplementarySlackness(), "Complementary slackness conditions are not met.");
3.90 -
3.91 - surb_test.getPath(P,0);
3.92 - check(P.length() == 4, "First path should contain 4 edges.");
3.93 -
3.94 - cout << (passed ? "All tests passed." : "Some of the tests failed!!!")
3.95 - << endl;
3.96 -
3.97 - return passed ? 0 : 1;
3.98 -
3.99 -}