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//======================================================================= // Copyright 2008 // Author: Matyas W Egyhazy // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) //======================================================================= #ifndef BOOST_GRAPH_METRIC_TSP_APPROX_HPP #define BOOST_GRAPH_METRIC_TSP_APPROX_HPP // metric_tsp_approx // Generates an approximate tour solution for the traveling salesperson // problem in polynomial time. The current algorithm guarantees a tour with a // length at most as long as 2x optimal solution. The graph should have // 'natural' (metric) weights such that the triangle inequality is maintained. // Graphs must be fully interconnected. // TODO: // There are a couple of improvements that could be made. // 1) Change implementation to lower uppper bound Christofides heuristic // 2) Implement a less restrictive TSP heuristic (one that does not rely on // triangle inequality). // 3) Determine if the algorithm can be implemented without creating a new // graph. #include #include #include #include #include #include #include #include #include namespace boost { // Define a concept for the concept-checking library. template < typename Visitor, typename Graph > struct TSPVertexVisitorConcept { private: Visitor vis_; public: typedef typename graph_traits< Graph >::vertex_descriptor Vertex; BOOST_CONCEPT_USAGE(TSPVertexVisitorConcept) { Visitor vis(vis_); // require copy construction Graph g(1); Vertex v(*vertices(g).first); vis.visit_vertex(v, g); // require visit_vertex } }; // Tree visitor that keeps track of a preorder traversal of a tree // TODO: Consider migrating this to the graph_as_tree header. // TODO: Parameterize the underlying stores so it doesn't have to be a vector. template < typename Node, typename Tree > class PreorderTraverser { private: std::vector< Node >& path_; public: typedef typename std::vector< Node >::const_iterator const_iterator; PreorderTraverser(std::vector< Node >& p) : path_(p) {} void preorder(Node n, const Tree&) { path_.push_back(n); } void inorder(Node, const Tree&) const {} void postorder(Node, const Tree&) const {} const_iterator begin() const { return path_.begin(); } const_iterator end() const { return path_.end(); } }; // Forward declarations template < typename > class tsp_tour_visitor; template < typename, typename, typename, typename > class tsp_tour_len_visitor; template < typename VertexListGraph, typename OutputIterator > void metric_tsp_approx_tour(VertexListGraph& g, OutputIterator o) { metric_tsp_approx_from_vertex(g, *vertices(g).first, get(edge_weight, g), get(vertex_index, g), tsp_tour_visitor< OutputIterator >(o)); } template < typename VertexListGraph, typename WeightMap, typename OutputIterator > void metric_tsp_approx_tour(VertexListGraph& g, WeightMap w, OutputIterator o) { metric_tsp_approx_from_vertex( g, *vertices(g).first, w, tsp_tour_visitor< OutputIterator >(o)); } template < typename VertexListGraph, typename OutputIterator > void metric_tsp_approx_tour_from_vertex(VertexListGraph& g, typename graph_traits< VertexListGraph >::vertex_descriptor start, OutputIterator o) { metric_tsp_approx_from_vertex(g, start, get(edge_weight, g), get(vertex_index, g), tsp_tour_visitor< OutputIterator >(o)); } template < typename VertexListGraph, typename WeightMap, typename OutputIterator > void metric_tsp_approx_tour_from_vertex(VertexListGraph& g, typename graph_traits< VertexListGraph >::vertex_descriptor start, WeightMap w, OutputIterator o) { metric_tsp_approx_from_vertex(g, start, w, get(vertex_index, g), tsp_tour_visitor< OutputIterator >(o)); } template < typename VertexListGraph, typename TSPVertexVisitor > void metric_tsp_approx(VertexListGraph& g, TSPVertexVisitor vis) { metric_tsp_approx_from_vertex( g, *vertices(g).first, get(edge_weight, g), get(vertex_index, g), vis); } template < typename VertexListGraph, typename Weightmap, typename VertexIndexMap, typename TSPVertexVisitor > void metric_tsp_approx(VertexListGraph& g, Weightmap w, TSPVertexVisitor vis) { metric_tsp_approx_from_vertex( g, *vertices(g).first, w, get(vertex_index, g), vis); } template < typename VertexListGraph, typename WeightMap, typename VertexIndexMap, typename TSPVertexVisitor > void metric_tsp_approx( VertexListGraph& g, WeightMap w, VertexIndexMap id, TSPVertexVisitor vis) { metric_tsp_approx_from_vertex(g, *vertices(g).first, w, id, vis); } template < typename VertexListGraph, typename WeightMap, typename TSPVertexVisitor > void metric_tsp_approx_from_vertex(VertexListGraph& g, typename graph_traits< VertexListGraph >::vertex_descriptor start, WeightMap w, TSPVertexVisitor vis) { metric_tsp_approx_from_vertex(g, start, w, get(vertex_index, g), vis); } template < typename VertexListGraph, typename WeightMap, typename VertexIndexMap, typename TSPVertexVisitor > void metric_tsp_approx_from_vertex(const VertexListGraph& g, typename graph_traits< VertexListGraph >::vertex_descriptor start, WeightMap weightmap, VertexIndexMap indexmap, TSPVertexVisitor vis) { using namespace boost; using namespace std; BOOST_CONCEPT_ASSERT((VertexListGraphConcept< VertexListGraph >)); BOOST_CONCEPT_ASSERT( (TSPVertexVisitorConcept< TSPVertexVisitor, VertexListGraph >)); // Types related to the input graph (GVertex is a template parameter). typedef typename graph_traits< VertexListGraph >::vertex_descriptor GVertex; typedef typename graph_traits< VertexListGraph >::vertex_iterator GVItr; // We build a custom graph in this algorithm. typedef adjacency_list< vecS, vecS, directedS, no_property, no_property > MSTImpl; typedef graph_traits< MSTImpl >::vertex_descriptor Vertex; typedef graph_traits< MSTImpl >::vertex_iterator VItr; // And then re-cast it as a tree. typedef iterator_property_map< vector< Vertex >::iterator, property_map< MSTImpl, vertex_index_t >::type > ParentMap; typedef graph_as_tree< MSTImpl, ParentMap > Tree; typedef tree_traits< Tree >::node_descriptor Node; // A predecessor map. typedef vector< GVertex > PredMap; typedef iterator_property_map< typename PredMap::iterator, VertexIndexMap > PredPMap; PredMap preds(num_vertices(g)); PredPMap pred_pmap(preds.begin(), indexmap); // Compute a spanning tree over the in put g. prim_minimum_spanning_tree(g, pred_pmap, root_vertex(start).vertex_index_map(indexmap).weight_map(weightmap)); // Build a MST using the predecessor map from prim mst MSTImpl mst(num_vertices(g)); std::size_t cnt = 0; pair< VItr, VItr > mst_verts(vertices(mst)); for (typename PredMap::iterator vi(preds.begin()); vi != preds.end(); ++vi, ++cnt) { if (indexmap[*vi] != cnt) { add_edge(*next(mst_verts.first, indexmap[*vi]), *next(mst_verts.first, cnt), mst); } } // Build a tree abstraction over the MST. vector< Vertex > parent(num_vertices(mst)); Tree t(mst, *vertices(mst).first, make_iterator_property_map(parent.begin(), get(vertex_index, mst))); // Create tour using a preorder traversal of the mst vector< Node > tour; PreorderTraverser< Node, Tree > tvis(tour); traverse_tree(indexmap[start], t, tvis); pair< GVItr, GVItr > g_verts(vertices(g)); for (PreorderTraverser< Node, Tree >::const_iterator curr(tvis.begin()); curr != tvis.end(); ++curr) { // TODO: This is will be O(n^2) if vertex storage of g != vecS. GVertex v = *next(g_verts.first, get(vertex_index, mst)[*curr]); vis.visit_vertex(v, g); } // Connect back to the start of the tour vis.visit_vertex(start, g); } // Default tsp tour visitor that puts the tour in an OutputIterator template < typename OutItr > class tsp_tour_visitor { OutItr itr_; public: tsp_tour_visitor(OutItr itr) : itr_(itr) {} template < typename Vertex, typename Graph > void visit_vertex(Vertex v, const Graph&) { BOOST_CONCEPT_ASSERT((OutputIterator< OutItr, Vertex >)); *itr_++ = v; } }; // Tsp tour visitor that adds the total tour length. template < typename Graph, typename WeightMap, typename OutIter, typename Length > class tsp_tour_len_visitor { typedef typename graph_traits< Graph >::vertex_descriptor Vertex; BOOST_CONCEPT_ASSERT((OutputIterator< OutIter, Vertex >)); OutIter iter_; Length& tourlen_; WeightMap& wmap_; Vertex previous_; // Helper function for getting the null vertex. Vertex null() { return graph_traits< Graph >::null_vertex(); } public: tsp_tour_len_visitor(Graph const&, OutIter iter, Length& l, WeightMap& map) : iter_(iter), tourlen_(l), wmap_(map), previous_(null()) { } void visit_vertex(Vertex v, const Graph& g) { typedef typename graph_traits< Graph >::edge_descriptor Edge; // If it is not the start, then there is a // previous vertex if (previous_ != null()) { // NOTE: For non-adjacency matrix graphs g, this bit of code // will be linear in the degree of previous_ or v. A better // solution would be to visit edges of the graph, but that // would require revisiting the core algorithm. Edge e; bool found; boost::tie(e, found) = lookup_edge(previous_, v, g); if (!found) { BOOST_THROW_EXCEPTION(not_complete()); } tourlen_ += wmap_[e]; } previous_ = v; *iter_++ = v; } }; // Object generator(s) template < typename OutIter > inline tsp_tour_visitor< OutIter > make_tsp_tour_visitor(OutIter iter) { return tsp_tour_visitor< OutIter >(iter); } template < typename Graph, typename WeightMap, typename OutIter, typename Length > inline tsp_tour_len_visitor< Graph, WeightMap, OutIter, Length > make_tsp_tour_len_visitor( Graph const& g, OutIter iter, Length& l, WeightMap map) { return tsp_tour_len_visitor< Graph, WeightMap, OutIter, Length >( g, iter, l, map); } } // boost #endif // BOOST_GRAPH_METRIC_TSP_APPROX_HPP