COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/steiner.h @ 2510:bb523a4758f7

Last change on this file since 2510:bb523a4758f7 was 2510:bb523a4758f7, checked in by Balazs Dezso, 12 years ago

removing semicolon ftom the end of GRAPH_TYPEDEFS

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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
31#include <lemon/ugraph_adaptor.h>
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    Value _value;
130
131  public:
132
133    /// \brief Constructor
134   
135    /// Constructor
136    ///
137    SteinerTree(const UGraph &graph, const CostMap &cost)
138      : _graph(graph), _cost(cost), _dijkstra(graph, _cost),
139        _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {}
140
141    /// \brief Initializes the internal data structures.
142    ///
143    /// Initializes the internal data structures.
144    void init() {
145      if (!_pred) _pred = new PredMap(_graph);
146      if (!_comp) _comp = new CompMap(_graph);
147      if (!_forked) _forked = new ForkedMap(*_pred, *_comp);
148      if (!_filter) _filter = new FilterMap(_graph);
149      if (!_tree) _tree = new TreeMap(_graph);
150      _dijkstra.predMap(*_forked);
151      _dijkstra.init();
152      _terminal_num = 0;
153      for (NodeIt it(_graph); it != INVALID; ++it) {
154        _filter->set(it, false);
155      }
156    }
157
158    /// \brief Adds a new terminal node.
159    ///
160    /// Adds a new terminal node to the Steiner-tree problem.
161    void addTerminal(const Node& node) {
162      if (!_dijkstra.reached(node)) {
163        _dijkstra.addSource(node);
164        _comp->comp(node, _terminal_num);
165        ++_terminal_num;
166      }
167    }
168   
169    /// \brief Executes the algorithm.
170    ///
171    /// Executes the algorithm.
172    ///
173    /// \pre init() must be called and at least some nodes should be
174    /// added with addTerminal() before using this function.
175    ///
176    /// This method constructs an approximation of the Steiner-Tree.
177    void start() {
178      _dijkstra.start();
179     
180      std::vector<External> externals;
181      for (UEdgeIt it(_graph); it != INVALID; ++it) {
182        Node s = _graph.source(it);
183        Node t = _graph.target(it);
184        if (_comp->comp(s) == _comp->comp(t)) continue;
185
186        Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it];
187
188        if (_comp->comp(s) < _comp->comp(t)) {
189          externals.push_back(External(_comp->comp(s), _comp->comp(t),
190                                       it, cost));
191        } else {
192          externals.push_back(External(_comp->comp(t), _comp->comp(s),
193                                       it, cost));
194        }
195      }
196      std::sort(externals.begin(), externals.end(), ExternalLess());
197
198      SmartUGraph aux_graph;
199      std::vector<SmartUGraph::Node> aux_nodes;
200
201      for (int i = 0; i < _terminal_num; ++i) {
202        aux_nodes.push_back(aux_graph.addNode());
203      }
204
205      SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph);
206      SmartUGraph::UEdgeMap<UEdge> cross(aux_graph);
207      {
208        int i = 0;
209        while (i < int(externals.size())) {
210          int sn = externals[i].source;
211          int tn = externals[i].target;
212          Value ev = externals[i].value;
213          UEdge ee = externals[i].uedge;
214          ++i;
215          while (i < int(externals.size()) &&
216                 sn == externals[i].source && tn == externals[i].target) {
217            if (externals[i].value < ev) {
218              ev = externals[i].value;
219              ee = externals[i].uedge;
220            }
221            ++i;
222          }
223          SmartUGraph::UEdge ne =
224            aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]);
225          aux_cost.set(ne, ev);
226          cross.set(ne, ee);
227        }
228      }
229
230      std::vector<SmartUGraph::UEdge> aux_tree_edges;
231      BackInserterBoolMap<std::vector<SmartUGraph::UEdge> >
232        aux_tree_map(aux_tree_edges);
233      prim(aux_graph, aux_cost, aux_tree_map);
234
235      for (std::vector<SmartUGraph::UEdge>::iterator
236             it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) {
237        Node node;
238        node = _graph.source(cross[*it]);
239        while (node != INVALID && !(*_filter)[node]) {
240          _filter->set(node, true);
241          node = (*_pred)[node] != INVALID ?
242            _graph.source((*_pred)[node]) : INVALID;
243        }
244        node = _graph.target(cross[*it]);
245        while (node != INVALID && !(*_filter)[node]) {
246          _filter->set(node, true);
247          node = (*_pred)[node] != INVALID ?
248            _graph.source((*_pred)[node]) : INVALID;
249        }
250      }
251
252      _value = prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree);
253           
254    }
255
256    /// \brief Checks if an edge is in the Steiner-tree or not.
257    ///
258    /// Checks if an edge is in the Steiner-tree or not.
259    /// \param e is the edge that will be checked
260    /// \return \c true if e is in the Steiner-tree, \c false otherwise
261    bool tree(UEdge e){
262      return (*_tree)[e];
263    }
264
265    /// \brief Checks if the node is in the Steiner-tree or not.
266    ///
267    /// Checks if a node is in the Steiner-tree or not.
268    /// \param n is the node that will be checked
269    /// \return \c true if n is in the Steiner-tree, \c false otherwise
270    bool tree(Node n){
271      return (*_filter)[n];
272    }
273
274    /// \brief Checks if the node is a Steiner-node.
275    ///
276    /// Checks if the node is a Steiner-node (i.e. a tree node but
277    /// not terminal).
278    /// \param n is the node that will be checked
279    /// \return \c true if n is a Steiner-node, \c false otherwise
280    bool steiner(Node n){
281      return (*_filter)[n] && (*_pred)[n] != INVALID;
282    }
283
284    /// \brief Checks if the node is a terminal.
285    ///
286    /// Checks if the node is a terminal.
287    /// \param n is the node that will be checked
288    /// \return \c true if n is a terminal, \c false otherwise
289    bool terminal(Node n){
290      return _dijkstra.reached(n) && (*_pred)[n] == INVALID;
291    }
292   
293    /// \brief The total cost of the tree
294    ///
295    /// The total cost of the constructed tree. The calculated value does
296    /// not exceed the double of the optimal value.
297    Value treeValue() const {
298      return _value;
299    }
300   
301  };
302
303} //END OF NAMESPACE LEMON
304
305#endif
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