1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/steiner.h Thu Mar 01 16:47:49 2007 +0000
1.3 @@ -0,0 +1,277 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2006
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_STEINER_H
1.23 +#define LEMON_STEINER_H
1.24 +
1.25 +///\ingroup approx
1.26 +///\file
1.27 +///\brief Algorithm for the 2-approximation of Steiner Tree problem.
1.28 +///
1.29 +
1.30 +#include <lemon/smart_graph.h>
1.31 +#include <lemon/graph_utils.h>
1.32 +#include <lemon/error.h>
1.33 +
1.34 +#include <lemon/ugraph_adaptor.h>
1.35 +#include <lemon/maps.h>
1.36 +
1.37 +#include <lemon/dijkstra.h>
1.38 +#include <lemon/prim.h>
1.39 +
1.40 +
1.41 +namespace lemon {
1.42 +
1.43 + /// \ingroup approx
1.44 +
1.45 + /// \brief Algorithm for the 2-approximation of Steiner Tree problem
1.46 + ///
1.47 + /// The Steiner-tree problem is the next: Given a connected
1.48 + /// undirected graph, a cost function on the edges and a subset of
1.49 + /// the nodes. Construct a tree with minimum cost which covers the
1.50 + /// given subset of the nodes. The problem is NP-hard moreover
1.51 + /// it is APX-complete too.
1.52 + ///
1.53 + /// Mehlhorn's approximation algorithm is implemented in this class,
1.54 + /// which gives a 2-approximation for the Steiner-tree problem. The
1.55 + /// algorithm's time complexity is O(nlog(n)+e).
1.56 + template <typename UGraph,
1.57 + typename CostMap = typename UGraph:: template UEdgeMap<double> >
1.58 + class SteinerTree {
1.59 + public:
1.60 +
1.61 + UGRAPH_TYPEDEFS(typename UGraph)
1.62 +
1.63 + typedef typename CostMap::Value Value;
1.64 +
1.65 + private:
1.66 +
1.67 + class CompMap {
1.68 + public:
1.69 + typedef Node Key;
1.70 + typedef Edge Value;
1.71 +
1.72 + private:
1.73 + const UGraph& _graph;
1.74 + typename UGraph::template NodeMap<int> _comp;
1.75 +
1.76 + public:
1.77 + CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {}
1.78 +
1.79 + void set(const Node& node, const Edge& edge) {
1.80 + if (edge != INVALID) {
1.81 + _comp.set(node, _comp[_graph.source(edge)]);
1.82 + } else {
1.83 + _comp.set(node, -1);
1.84 + }
1.85 + }
1.86 +
1.87 + int comp(const Node& node) const { return _comp[node]; }
1.88 + void comp(const Node& node, int value) { _comp.set(node, value); }
1.89 + };
1.90 +
1.91 + typedef typename UGraph::template NodeMap<Edge> PredMap;
1.92 +
1.93 + typedef ForkWriteMap<PredMap, CompMap> ForkedMap;
1.94 +
1.95 +
1.96 + struct External {
1.97 + int source, target;
1.98 + UEdge uedge;
1.99 + Value value;
1.100 +
1.101 + External(int s, int t, const UEdge& e, const Value& v)
1.102 + : source(s), target(t), uedge(e), value(v) {}
1.103 + };
1.104 +
1.105 + struct ExternalLess {
1.106 + bool operator()(const External& left, const External& right) const {
1.107 + return (left.source < right.source) ||
1.108 + (left.source == right.source && left.target < right.target);
1.109 + }
1.110 + };
1.111 +
1.112 +
1.113 + typedef typename UGraph::template NodeMap<bool> FilterMap;
1.114 +
1.115 + typedef typename UGraph::template UEdgeMap<bool> TreeMap;
1.116 +
1.117 + const UGraph& _graph;
1.118 + const CostMap& _cost;
1.119 +
1.120 + typename Dijkstra<UGraph, CostMap>::
1.121 + template DefPredMap<ForkedMap>::Create _dijkstra;
1.122 +
1.123 + PredMap* _pred;
1.124 + CompMap* _comp;
1.125 + ForkedMap* _forked;
1.126 +
1.127 + int _terminal_num;
1.128 +
1.129 + FilterMap *_filter;
1.130 + TreeMap *_tree;
1.131 +
1.132 + public:
1.133 +
1.134 + /// \brief Constructor
1.135 +
1.136 + /// Constructor
1.137 + ///
1.138 + SteinerTree(const UGraph &graph, const CostMap &cost)
1.139 + : _graph(graph), _cost(cost), _dijkstra(graph, _cost),
1.140 + _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {}
1.141 +
1.142 + /// \brief Initializes the internal data structures.
1.143 + ///
1.144 + /// Initializes the internal data structures.
1.145 + void init() {
1.146 + if (!_pred) _pred = new PredMap(_graph);
1.147 + if (!_comp) _comp = new CompMap(_graph);
1.148 + if (!_forked) _forked = new ForkedMap(*_pred, *_comp);
1.149 + if (!_filter) _filter = new FilterMap(_graph);
1.150 + if (!_tree) _tree = new TreeMap(_graph);
1.151 + _dijkstra.predMap(*_forked);
1.152 + _dijkstra.init();
1.153 + _terminal_num = 0;
1.154 + for (NodeIt it(_graph); it != INVALID; ++it) {
1.155 + _filter->set(it, false);
1.156 + }
1.157 + }
1.158 +
1.159 + /// \brief Adds a new terminal node.
1.160 + ///
1.161 + /// Adds a new terminal node to the Steiner-tree problem.
1.162 + void addTerminal(const Node& node) {
1.163 + if (!_dijkstra.reached(node)) {
1.164 + _dijkstra.addSource(node);
1.165 + _comp->comp(node, _terminal_num);
1.166 + ++_terminal_num;
1.167 + }
1.168 + }
1.169 +
1.170 + /// \brief Executes the algorithm.
1.171 + ///
1.172 + /// Executes the algorithm.
1.173 + ///
1.174 + /// \pre init() must be called and at least some nodes should be
1.175 + /// added with addTerminal() before using this function.
1.176 + ///
1.177 + /// This method constructs an approximation of the Steiner-Tree.
1.178 + void start() {
1.179 + _dijkstra.start();
1.180 +
1.181 + std::vector<External> externals;
1.182 + for (UEdgeIt it(_graph); it != INVALID; ++it) {
1.183 + Node s = _graph.source(it);
1.184 + Node t = _graph.target(it);
1.185 + if (_comp->comp(s) == _comp->comp(t)) continue;
1.186 +
1.187 + Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it];
1.188 +
1.189 + if (_comp->comp(s) < _comp->comp(t)) {
1.190 + externals.push_back(External(_comp->comp(s), _comp->comp(t),
1.191 + it, cost));
1.192 + } else {
1.193 + externals.push_back(External(_comp->comp(t), _comp->comp(s),
1.194 + it, cost));
1.195 + }
1.196 + }
1.197 + std::sort(externals.begin(), externals.end(), ExternalLess());
1.198 +
1.199 + SmartUGraph aux_graph;
1.200 + std::vector<SmartUGraph::Node> aux_nodes;
1.201 +
1.202 + for (int i = 0; i < _terminal_num; ++i) {
1.203 + aux_nodes.push_back(aux_graph.addNode());
1.204 + }
1.205 +
1.206 + SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph);
1.207 + SmartUGraph::UEdgeMap<UEdge> cross(aux_graph);
1.208 + {
1.209 + int i = 0;
1.210 + while (i < (int)externals.size()) {
1.211 + int sn = externals[i].source;
1.212 + int tn = externals[i].target;
1.213 + Value ev = externals[i].value;
1.214 + UEdge ee = externals[i].uedge;
1.215 + ++i;
1.216 + while (i < (int)externals.size() &&
1.217 + sn == externals[i].source && tn == externals[i].target) {
1.218 + if (externals[i].value < ev) {
1.219 + ev = externals[i].value;
1.220 + ee = externals[i].uedge;
1.221 + }
1.222 + ++i;
1.223 + }
1.224 + SmartUGraph::UEdge ne =
1.225 + aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]);
1.226 + aux_cost.set(ne, ev);
1.227 + cross.set(ne, ee);
1.228 + }
1.229 + }
1.230 +
1.231 + std::vector<SmartUGraph::UEdge> aux_tree_edges;
1.232 + BackInserterBoolMap<std::vector<SmartUGraph::UEdge> >
1.233 + aux_tree_map(aux_tree_edges);
1.234 + prim(aux_graph, aux_cost, aux_tree_map);
1.235 +
1.236 + for (std::vector<SmartUGraph::UEdge>::iterator
1.237 + it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) {
1.238 + Node node;
1.239 + node = _graph.source(cross[*it]);
1.240 + while (node != INVALID && !(*_filter)[node]) {
1.241 + _filter->set(node, true);
1.242 + node = (*_pred)[node] != INVALID ?
1.243 + _graph.source((*_pred)[node]) : INVALID;
1.244 + }
1.245 + node = _graph.target(cross[*it]);
1.246 + while (node != INVALID && !(*_filter)[node]) {
1.247 + _filter->set(node, true);
1.248 + node = (*_pred)[node] != INVALID ?
1.249 + _graph.source((*_pred)[node]) : INVALID;
1.250 + }
1.251 + }
1.252 +
1.253 + prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree);
1.254 +
1.255 + }
1.256 +
1.257 + /// \brief Checks if an edge is in the Steiner-tree or not.
1.258 + ///
1.259 + /// Checks if an edge is in the Steiner-tree or not.
1.260 + /// \param e is the edge that will be checked
1.261 + /// \return \c true if e is in the Steiner-tree, \c false otherwise
1.262 + bool tree(UEdge e){
1.263 + return (*_tree)[e];
1.264 + }
1.265 +
1.266 + /// \brief Checks if the node is in the Steiner-tree or not.
1.267 + ///
1.268 + /// Checks if a node is in the Steiner-tree or not.
1.269 + /// \param n is the node that will be checked
1.270 + /// \return \c true if n is in the Steiner-tree, \c false otherwise
1.271 + bool tree(Node n){
1.272 + return (*_filter)[n];
1.273 + }
1.274 +
1.275 +
1.276 + };
1.277 +
1.278 +} //END OF NAMESPACE LEMON
1.279 +
1.280 +#endif