Edit: /usr/include/boost/graph/metric_tsp_approx.hpp (10809B)
//=======================================================================
// 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