# source:lemon-0.x/lemon/steiner.h@2382:678bea23ed75

Last change on this file since 2382:678bea23ed75 was 2382:678bea23ed75, checked in by Balazs Dezso, 13 years ago

2-approximation of Steiner-tree problem

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_STEINER_H
20#define LEMON_STEINER_H
21
22///\ingroup approx
23///\file
24///\brief Algorithm for the 2-approximation of Steiner Tree problem.
25///
26
27#include <lemon/smart_graph.h>
28#include <lemon/graph_utils.h>
29#include <lemon/error.h>
30
32#include <lemon/maps.h>
33
34#include <lemon/dijkstra.h>
35#include <lemon/prim.h>
36
37
38namespace lemon {
39
40  /// \ingroup approx
41
42  /// \brief Algorithm for the 2-approximation of Steiner Tree problem
43  ///
44  /// The Steiner-tree problem is the next: Given a connected
45  /// undirected graph, a cost function on the edges and a subset of
46  /// the nodes. Construct a tree with minimum cost which covers the
47  /// given subset of the nodes. The problem is NP-hard moreover
48  /// it is APX-complete too.
49  ///
50  /// Mehlhorn's approximation algorithm is implemented in this class,
51  /// which gives a 2-approximation for the Steiner-tree problem. The
52  /// algorithm's time complexity is O(nlog(n)+e).
53  template <typename UGraph,
54            typename CostMap = typename UGraph:: template UEdgeMap<double> >
55  class SteinerTree {
56  public:
57
58    UGRAPH_TYPEDEFS(typename UGraph)
59
60    typedef typename CostMap::Value Value;
61
62  private:
63
64    class CompMap {
65    public:
66      typedef Node Key;
67      typedef Edge Value;
68
69    private:
70      const UGraph& _graph;
71      typename UGraph::template NodeMap<int> _comp;
72
73    public:
74      CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {}
75
76      void set(const Node& node, const Edge& edge) {
77        if (edge != INVALID) {
78          _comp.set(node, _comp[_graph.source(edge)]);
79        } else {
80          _comp.set(node, -1);
81        }
82      }
83
84      int comp(const Node& node) const { return _comp[node]; }
85      void comp(const Node& node, int value) { _comp.set(node, value); }
86    };
87
88    typedef typename UGraph::template NodeMap<Edge> PredMap;
89
90    typedef ForkWriteMap<PredMap, CompMap> ForkedMap;
91
92
93    struct External {
94      int source, target;
95      UEdge uedge;
96      Value value;
97
98      External(int s, int t, const UEdge& e, const Value& v)
99        : source(s), target(t), uedge(e), value(v) {}
100    };
101
102    struct ExternalLess {
103      bool operator()(const External& left, const External& right) const {
104        return (left.source < right.source) ||
105          (left.source == right.source && left.target < right.target);
106      }
107    };
108
109
110    typedef typename UGraph::template NodeMap<bool> FilterMap;
111
112    typedef typename UGraph::template UEdgeMap<bool> TreeMap;
113
114    const UGraph& _graph;
115    const CostMap& _cost;
116
117    typename Dijkstra<UGraph, CostMap>::
118    template DefPredMap<ForkedMap>::Create _dijkstra;
119
120    PredMap* _pred;
121    CompMap* _comp;
122    ForkedMap* _forked;
123
124    int _terminal_num;
125
126    FilterMap *_filter;
127    TreeMap *_tree;
128
129  public:
130
131    /// \brief Constructor
132
133    /// Constructor
134    ///
135    SteinerTree(const UGraph &graph, const CostMap &cost)
136      : _graph(graph), _cost(cost), _dijkstra(graph, _cost),
137        _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {}
138
139    /// \brief Initializes the internal data structures.
140    ///
141    /// Initializes the internal data structures.
142    void init() {
143      if (!_pred) _pred = new PredMap(_graph);
144      if (!_comp) _comp = new CompMap(_graph);
145      if (!_forked) _forked = new ForkedMap(*_pred, *_comp);
146      if (!_filter) _filter = new FilterMap(_graph);
147      if (!_tree) _tree = new TreeMap(_graph);
148      _dijkstra.predMap(*_forked);
149      _dijkstra.init();
150      _terminal_num = 0;
151      for (NodeIt it(_graph); it != INVALID; ++it) {
152        _filter->set(it, false);
153      }
154    }
155
156    /// \brief Adds a new terminal node.
157    ///
158    /// Adds a new terminal node to the Steiner-tree problem.
159    void addTerminal(const Node& node) {
160      if (!_dijkstra.reached(node)) {
162        _comp->comp(node, _terminal_num);
163        ++_terminal_num;
164      }
165    }
166
167    /// \brief Executes the algorithm.
168    ///
169    /// Executes the algorithm.
170    ///
171    /// \pre init() must be called and at least some nodes should be
173    ///
174    /// This method constructs an approximation of the Steiner-Tree.
175    void start() {
176      _dijkstra.start();
177
178      std::vector<External> externals;
179      for (UEdgeIt it(_graph); it != INVALID; ++it) {
180        Node s = _graph.source(it);
181        Node t = _graph.target(it);
182        if (_comp->comp(s) == _comp->comp(t)) continue;
183
184        Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it];
185
186        if (_comp->comp(s) < _comp->comp(t)) {
187          externals.push_back(External(_comp->comp(s), _comp->comp(t),
188                                       it, cost));
189        } else {
190          externals.push_back(External(_comp->comp(t), _comp->comp(s),
191                                       it, cost));
192        }
193      }
194      std::sort(externals.begin(), externals.end(), ExternalLess());
195
196      SmartUGraph aux_graph;
197      std::vector<SmartUGraph::Node> aux_nodes;
198
199      for (int i = 0; i < _terminal_num; ++i) {
201      }
202
203      SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph);
204      SmartUGraph::UEdgeMap<UEdge> cross(aux_graph);
205      {
206        int i = 0;
207        while (i < (int)externals.size()) {
208          int sn = externals[i].source;
209          int tn = externals[i].target;
210          Value ev = externals[i].value;
211          UEdge ee = externals[i].uedge;
212          ++i;
213          while (i < (int)externals.size() &&
214                 sn == externals[i].source && tn == externals[i].target) {
215            if (externals[i].value < ev) {
216              ev = externals[i].value;
217              ee = externals[i].uedge;
218            }
219            ++i;
220          }
221          SmartUGraph::UEdge ne =
223          aux_cost.set(ne, ev);
224          cross.set(ne, ee);
225        }
226      }
227
228      std::vector<SmartUGraph::UEdge> aux_tree_edges;
229      BackInserterBoolMap<std::vector<SmartUGraph::UEdge> >
230        aux_tree_map(aux_tree_edges);
231      prim(aux_graph, aux_cost, aux_tree_map);
232
233      for (std::vector<SmartUGraph::UEdge>::iterator
234             it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) {
235        Node node;
236        node = _graph.source(cross[*it]);
237        while (node != INVALID && !(*_filter)[node]) {
238          _filter->set(node, true);
239          node = (*_pred)[node] != INVALID ?
240            _graph.source((*_pred)[node]) : INVALID;
241        }
242        node = _graph.target(cross[*it]);
243        while (node != INVALID && !(*_filter)[node]) {
244          _filter->set(node, true);
245          node = (*_pred)[node] != INVALID ?
246            _graph.source((*_pred)[node]) : INVALID;
247        }
248      }
249
251
252    }
253
254    /// \brief Checks if an edge is in the Steiner-tree or not.
255    ///
256    /// Checks if an edge is in the Steiner-tree or not.
257    /// \param e is the edge that will be checked
258    /// \return \c true if e is in the Steiner-tree, \c false otherwise
259    bool tree(UEdge e){
260      return (*_tree)[e];
261    }
262
263    /// \brief Checks if the node is in the Steiner-tree or not.
264    ///
265    /// Checks if a node is in the Steiner-tree or not.
266    /// \param n is the node that will be checked
267    /// \return \c true if n is in the Steiner-tree, \c false otherwise
268    bool tree(Node n){
269      return (*_filter)[n];
270    }
271
272
273  };
274
275} //END OF NAMESPACE LEMON
276
277#endif
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