/Src/Dependencies/Boost/boost/graph/metric_tsp_approx.hpp

  1
  2//=======================================================================
  3// Copyright 2008
  4// Author: Matyas W Egyhazy
  5//
  6// Distributed under the Boost Software License, Version 1.0. (See
  7// accompanying file LICENSE_1_0.txt or copy at
  8// http://www.boost.org/LICENSE_1_0.txt)
  9//=======================================================================
 10
 11#ifndef BOOST_GRAPH_METRIC_TSP_APPROX_HPP
 12#define BOOST_GRAPH_METRIC_TSP_APPROX_HPP
 13
 14// metric_tsp_approx
 15// Generates an approximate tour solution for the traveling salesperson
 16// problem in polynomial time. The current algorithm guarantees a tour with a
 17// length at most as long as 2x optimal solution. The graph should have
 18// 'natural' (metric) weights such that the triangle inequality is maintained.
 19// Graphs must be fully interconnected.
 20
 21// TODO:
 22// There are a couple of improvements that could be made.
 23// 1) Change implementation to lower uppper bound Christofides heuristic
 24// 2) Implement a less restrictive TSP heuristic (one that does not rely on
 25//    triangle inequality).
 26// 3) Determine if the algorithm can be implemented without creating a new
 27//    graph.
 28
 29#include <vector>
 30
 31#include <boost/shared_ptr.hpp>
 32#include <boost/concept_check.hpp>
 33#include <boost/graph/graph_traits.hpp>
 34#include <boost/graph/graph_as_tree.hpp>
 35#include <boost/graph/adjacency_list.hpp>
 36#include <boost/graph/prim_minimum_spanning_tree.hpp>
 37#include <boost/graph/lookup_edge.hpp>
 38#include <boost/throw_exception.hpp>
 39
 40namespace boost
 41{
 42    // Define a concept for the concept-checking library.
 43    template <typename Visitor, typename Graph>
 44    struct TSPVertexVisitorConcept
 45    {
 46    private:
 47        Visitor vis_;
 48    public:
 49        typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
 50
 51        BOOST_CONCEPT_USAGE(TSPVertexVisitorConcept)
 52        {
 53            Visitor vis(vis_);  // require copy construction
 54            Graph g(1);
 55            Vertex v(*vertices(g).first);
 56            vis_.visit_vertex(v, g); // require visit_vertex
 57        }
 58    };
 59
 60    // Tree visitor that keeps track of a preorder traversal of a tree
 61    // TODO: Consider migrating this to the graph_as_tree header.
 62    // TODO: Parameterize the underlying stores o it doesn't have to be a vector.
 63    template<typename Node, typename Tree> class PreorderTraverser
 64    {
 65    private:
 66        std::vector<Node>& path_;
 67    public:
 68        typedef typename std::vector<Node>::const_iterator const_iterator;
 69
 70        PreorderTraverser(std::vector<Node>& p) : path_(p) {}
 71
 72        void preorder(Node n, const Tree&)
 73        { path_.push_back(n); }
 74
 75        void inorder(Node, const Tree&) const {}
 76        void postorder(Node, const Tree&) const {}
 77
 78        const_iterator begin() const { return path_.begin(); }
 79        const_iterator end() const { return path_.end(); }
 80    };
 81
 82    // Forward declarations
 83    template <typename> class tsp_tour_visitor;
 84    template <typename, typename, typename, typename> class tsp_tour_len_visitor;
 85
 86    template<typename VertexListGraph, typename OutputIterator>
 87    void metric_tsp_approx_tour(VertexListGraph& g, OutputIterator o)
 88    {
 89        metric_tsp_approx_from_vertex(g, *vertices(g).first,
 90            get(edge_weight, g), get(vertex_index, g),
 91            tsp_tour_visitor<OutputIterator>(o));
 92    }
 93
 94    template<typename VertexListGraph, typename WeightMap, typename OutputIterator>
 95    void metric_tsp_approx_tour(VertexListGraph& g, WeightMap w, OutputIterator o)
 96    {
 97        metric_tsp_approx_from_vertex(g, *vertices(g).first,
 98            w, tsp_tour_visitor<OutputIterator>(o));
 99    }
100
101    template<typename VertexListGraph, typename OutputIterator>
102    void metric_tsp_approx_tour_from_vertex(VertexListGraph& g,
103        typename graph_traits<VertexListGraph>::vertex_descriptor start,
104        OutputIterator o)
105    {
106        metric_tsp_approx_from_vertex(g, start, get(edge_weight, g),
107            get(vertex_index, g), tsp_tour_visitor<OutputIterator>(o));
108    }
109
110    template<typename VertexListGraph, typename WeightMap,
111        typename OutputIterator>
112    void metric_tsp_approx_tour_from_vertex(VertexListGraph& g,
113    typename graph_traits<VertexListGraph>::vertex_descriptor start,
114        WeightMap w, OutputIterator o)
115    {
116        metric_tsp_approx_from_vertex(g, start, w, get(vertex_index, g),
117            tsp_tour_visitor<OutputIterator>(o));
118    }
119
120    template<typename VertexListGraph, typename TSPVertexVisitor>
121    void metric_tsp_approx(VertexListGraph& g, TSPVertexVisitor vis)
122    {
123        metric_tsp_approx_from_vertex(g, *vertices(g).first,
124            get(edge_weight, g), get(vertex_index, g), vis);
125    }
126
127    template<typename VertexListGraph, typename Weightmap,
128        typename VertexIndexMap, typename TSPVertexVisitor>
129    void metric_tsp_approx(VertexListGraph& g, Weightmap w,
130        TSPVertexVisitor vis)
131    {
132        metric_tsp_approx_from_vertex(g, *vertices(g).first, w,
133            get(vertex_index, g), vis);
134    }
135
136    template<typename VertexListGraph, typename WeightMap,
137        typename VertexIndexMap, typename TSPVertexVisitor>
138    void metric_tsp_approx(VertexListGraph& g, WeightMap w, VertexIndexMap id,
139        TSPVertexVisitor vis)
140    {
141        metric_tsp_approx_from_vertex(g, *vertices(g).first, w, id, vis);
142    }
143
144    template<typename VertexListGraph, typename WeightMap,
145        typename TSPVertexVisitor>
146    void metric_tsp_approx_from_vertex(VertexListGraph& g,
147    typename graph_traits<VertexListGraph>::vertex_descriptor start,
148        WeightMap w, TSPVertexVisitor vis)
149    {
150        metric_tsp_approx_from_vertex(g, start, w, get(vertex_index, g), vis);
151    }
152
153    template <
154        typename VertexListGraph,
155        typename WeightMap,
156        typename VertexIndexMap,
157        typename TSPVertexVisitor>
158    void metric_tsp_approx_from_vertex(const VertexListGraph& g,
159                                       typename graph_traits<VertexListGraph>::vertex_descriptor start,
160                                       WeightMap weightmap,
161                                       VertexIndexMap indexmap,
162                                       TSPVertexVisitor vis)
163    {
164        using namespace boost;
165        using namespace std;
166
167        BOOST_CONCEPT_ASSERT((VertexListGraphConcept<VertexListGraph>));
168        BOOST_CONCEPT_ASSERT((TSPVertexVisitorConcept<TSPVertexVisitor, VertexListGraph>));
169
170        // Types related to the input graph (GVertex is a template parameter).
171        typedef typename graph_traits<VertexListGraph>::vertex_descriptor GVertex;
172        typedef typename graph_traits<VertexListGraph>::vertex_iterator GVItr;
173
174        // We build a custom graph in this algorithm.
175        typedef adjacency_list <vecS, vecS, directedS, no_property, no_property > MSTImpl;
176        typedef graph_traits<MSTImpl>::edge_descriptor Edge;
177        typedef graph_traits<MSTImpl>::vertex_descriptor Vertex;
178        typedef graph_traits<MSTImpl>::vertex_iterator VItr;
179
180        // And then re-cast it as a tree.
181        typedef iterator_property_map<vector<Vertex>::iterator, property_map<MSTImpl, vertex_index_t>::type> ParentMap;
182        typedef graph_as_tree<MSTImpl, ParentMap> Tree;
183        typedef tree_traits<Tree>::node_descriptor Node;
184
185        // A predecessor map.
186        typedef vector<GVertex> PredMap;
187        typedef iterator_property_map<typename PredMap::iterator, VertexIndexMap> PredPMap;
188
189        PredMap preds(num_vertices(g));
190        PredPMap pred_pmap(preds.begin(), indexmap);
191
192        // Compute a spanning tree over the in put g.
193        prim_minimum_spanning_tree(g, pred_pmap,
194             root_vertex(start)
195            .vertex_index_map(indexmap)
196            .weight_map(weightmap));
197
198        // Build a MST using the predecessor map from prim mst
199        MSTImpl mst(num_vertices(g));
200        std::size_t cnt = 0;
201        pair<VItr, VItr> mst_verts(vertices(mst));
202        for(typename PredMap::iterator vi(preds.begin()); vi != preds.end(); ++vi, ++cnt)
203        {
204            if(indexmap[*vi] != cnt) {
205                add_edge(*next(mst_verts.first, indexmap[*vi]),
206                         *next(mst_verts.first, cnt), mst);
207            }
208        }
209
210        // Build a tree abstraction over the MST.
211        vector<Vertex> parent(num_vertices(mst));
212        Tree t(mst, *vertices(mst).first,
213            make_iterator_property_map(parent.begin(),
214            get(vertex_index, mst)));
215
216        // Create tour using a preorder traversal of the mst
217        vector<Node> tour;
218        PreorderTraverser<Node, Tree> tvis(tour);
219        traverse_tree(0, t, tvis);
220
221        pair<GVItr, GVItr> g_verts(vertices(g));
222        for(PreorderTraverser<Node, Tree>::const_iterator curr(tvis.begin());
223            curr != tvis.end(); ++curr)
224        {
225            // TODO: This is will be O(n^2) if vertex storage of g != vecS.
226            GVertex v = *next(g_verts.first, get(vertex_index, mst)[*curr]);
227            vis.visit_vertex(v, g);
228        }
229
230        // Connect back to the start of the tour
231        vis.visit_vertex(*g_verts.first, g);
232    }
233
234    // Default tsp tour visitor that puts the tour in an OutputIterator
235    template <typename OutItr>
236    class tsp_tour_visitor
237    {
238        OutItr itr_;
239    public:
240        tsp_tour_visitor(OutItr itr)
241            : itr_(itr)
242        { }
243
244        template <typename Vertex, typename Graph>
245        void visit_vertex(Vertex v, const Graph&)
246        {
247            BOOST_CONCEPT_ASSERT((OutputIterator<OutItr, Vertex>));
248            *itr_++ = v;
249        }
250
251    };
252
253    // Tsp tour visitor that adds the total tour length.
254    template<typename Graph, typename WeightMap, typename OutIter, typename Length>
255    class tsp_tour_len_visitor
256    {
257        typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
258        BOOST_CONCEPT_ASSERT((OutputIterator<OutIter, Vertex>));
259
260        OutIter iter_;
261        Length& tourlen_;
262        WeightMap& wmap_;
263        Vertex previous_;
264
265        // Helper function for getting the null vertex.
266        Vertex null()
267        { return graph_traits<Graph>::null_vertex(); }
268
269    public:
270        tsp_tour_len_visitor(Graph const&, OutIter iter, Length& l, WeightMap map)
271            : iter_(iter), tourlen_(l), wmap_(map), previous_(null())
272        { }
273
274        void visit_vertex(Vertex v, const Graph& g)
275        {
276            typedef typename graph_traits<Graph>::edge_descriptor Edge;
277
278            // If it is not the start, then there is a
279            // previous vertex
280            if(previous_ != null())
281            {
282                // NOTE: For non-adjacency matrix graphs g, this bit of code
283                // will be linear in the degree of previous_ or v. A better
284                // solution would be to visit edges of the graph, but that
285                // would require revisiting the core algorithm.
286                Edge e;
287                bool found;
288                boost::tie(e, found) = lookup_edge(previous_, v, g);
289                if(!found) {
290                    BOOST_THROW_EXCEPTION(not_complete());
291                }
292
293                tourlen_ += wmap_[e];
294            }
295
296            previous_ = v;
297            *iter_++ = v;
298        }
299    };
300
301    // Object generator(s)
302    template <typename OutIter>
303    inline tsp_tour_visitor<OutIter>
304    make_tsp_tour_visitor(OutIter iter)
305    { return tsp_tour_visitor<OutIter>(iter); }
306
307    template <typename Graph, typename WeightMap, typename OutIter, typename Length>
308    inline tsp_tour_len_visitor<Graph, WeightMap, OutIter, Length>
309    make_tsp_tour_len_visitor(Graph const& g, OutIter iter, Length& l, WeightMap map)
310    { return tsp_tour_len_visitor<Graph, WeightMap, OutIter, Length>(g, iter, l, map); }
311
312} //boost
313
314#endif // BOOST_GRAPH_METRIC_TSP_APPROX_HPP