ColorMap in boost::graph implicit graph for metric_tsp_approx

Question

I'm trying to accomplish the following: Have a function computeTspTour(size, start, distance) that gives me an approximation to the shortest tour through size many vertices, starting at start. Here, distance is a function object that takes two indexes and returns the distance between them.

I would like to utilize boost::graph's metric_tsp_approx. For this, I need a complete graph of cardinality size, so I'd like to use an implicitly defined graph for this to avoid creating a useless trivial huge graph structure.

It all appears to work fine, but my problem is that metric_tsp_approx at some point uses dijkstra_shortest_paths, which defines a ColorMap. This leads to the following two problems:

/usr/include/boost/graph/dijkstra_shortest_paths.hpp:373:60: error: no type named 'value_type' in 'struct boost::property_traits<boost::bgl_named_params<boost::detail::_project2nd<double, double>, boost::distance_combine_t, boost::bgl_named_params<std::less<double>, boost::distance_compare_t, boost::bgl_named_params<boost::iterator_property_map<__gnu_cxx::__normal_iterator<long unsigned int*, std::vector<long unsigned int> >, boost::typed_identity_property_map<long unsigned int>, long unsigned int, long unsigned int&>, boost::vertex_predecessor_t, boost::bgl_named_params<EdgeWeightMap<double>, boost::edge_weight_t, boost::bgl_named_params<boost::typed_identity_property_map<long unsigned int>, boost::vertex_index_t, boost::bgl_named_params<long unsigned int, boost::root_vertex_t, boost::no_property> > > > > > >'
typedef typename property_traits<ColorMap>::value_type ColorValue;
                                                       ^

/usr/include/boost/graph/dijkstra_shortest_paths.hpp:374:38: error: no type named 'value_type' in 'struct boost::property_traits<boost::bgl_named_params<boost::detail::_project2nd<double, double>, boost::distance_combine_t, boost::bgl_named_params<std::less<double>, boost::distance_compare_t, boost::bgl_named_params<boost::iterator_property_map<__gnu_cxx::__normal_iterator<long unsigned int*, std::vector<long unsigned int> >, boost::typed_identity_property_map<long unsigned int>, long unsigned int, long unsigned int&>, boost::vertex_predecessor_t, boost::bgl_named_params<EdgeWeightMap<double>, boost::edge_weight_t, boost::bgl_named_params<boost::typed_identity_property_map<long unsigned int>, boost::vertex_index_t, boost::bgl_named_params<long unsigned int, boost::root_vertex_t, boost::no_property> > > > > > >'
typedef color_traits<ColorValue> Color;
                                 ^

However, I do not see how I could fix the traits of the ColorMap from where I am, creating a color property map on my own doesn't do any good.

The code that I use to create the implicit graph and running the tsp_metric_approx on it is the following. I apologize for its length, I hope it's straightforward. What it does is set up a class CompleteGraph, having one template parameter F that specifies the return type of the distance function. This class has the necessary iterators to be a VertexListGraph and an IncidenceGraph, so that tsp_metric_approx can run on it.

#include <algorithm>
#include <functional>
#include <iostream>
#include <iterator>
#include <vector>

#include <boost/iterator/iterator_facade.hpp>
#include <boost/graph/metric_tsp_approx.hpp>

using namespace boost;

typedef std::size_t VertexDescriptor;
typedef std::pair<VertexDescriptor, VertexDescriptor> EdgeDescriptor;

class VertexIterator : public boost::iterator_facade<VertexIterator, VertexDescriptor const, boost::bidirectional_traversal_tag>
{
    public:
        //! Default constructor
        VertexIterator() : pos_(0) {}

        //! Constructor setting the position
        explicit VertexIterator(VertexDescriptor pos) : pos_(pos) {}

        //! Dereference the iterator
        VertexDescriptor const& dereference() const { return pos_; }

        //! Check for equality
        bool equal(VertexIterator const& other) const { return pos_ == other.pos_; }

        //! Increment
        void increment() { ++pos_; }

        //! Decrement
        void decrement() { --pos_; }

    private:
        //! Grant access to boost::iterator_facade
        friend class boost::iterator_core_access;

        //! The current position
        VertexDescriptor pos_ = 0;
};

class OutEdgeIterator : public boost::iterator_facade<OutEdgeIterator, EdgeDescriptor const, boost::bidirectional_traversal_tag>
{
    public:
        //! Constructor setting the source vertex
        explicit OutEdgeIterator(VertexDescriptor source) { const std::size_t target = source == 0 ? 1 : 0; pos_ = EdgeDescriptor(source, target); }

        //! Constructor setting the source vertex and the target
        explicit OutEdgeIterator(VertexDescriptor source, VertexDescriptor target) : pos_(source, target) {}

        //! Dereference the iterator
        EdgeDescriptor const& dereference() const { return pos_; }

        //! Check for equality
        bool equal(OutEdgeIterator const& other) const { return pos_ == other.pos_; }

        //! Increment
        void increment() { ++pos_.second; if(pos_.first == pos_.second) { ++pos_.second; } }

        //! Decrement
        void decrement() { --pos_.second; if(pos_.first == pos_.second) { --pos_.second; } }

    private:
        //! Grant access to boost::iterator_facade
        friend class boost::iterator_core_access;

        //! The current edge
        EdgeDescriptor pos_ = EdgeDescriptor(0, 1);
};

//! Class representing a complete graph
/*!
 * This class works as a complete graph.
 * It defines a distance property map between any two points by calling the passed distance function.
 * \tparam F The return type of the distance function
 */
template<typename F>
class CompleteGraph
{
    public:
        typedef VertexDescriptor vertex_descriptor;
        typedef EdgeDescriptor edge_descriptor;
        typedef void adjacency_iterator;
        typedef OutEdgeIterator out_edge_iterator;
        typedef void in_edge_iterator;
        typedef void edge_iterator;
        typedef VertexIterator vertex_iterator;
        typedef std::size_t degree_size_type;
        typedef std::size_t vertices_size_type;
        typedef std::size_t edges_size_type;
        typedef undirected_tag directed_category;
        typedef disallow_parallel_edge_tag edge_parallel_category;
        typedef vertex_list_graph_tag traversal_category;

        //! Delete default constructor
        CompleteGraph() = delete;

        //! Constructor from a given size
        /*!
         * If no distance is specified, we default to a constant function returning F(1)
         */
        explicit CompleteGraph(std::size_t size) : size_(size), distance_(returnOne) {}

        //! Constructor from a given size and a distance function of type F
        /*!
         * The constructed graph will have size many vertices.
         * Its distance map will be of the following form: The distance between points i and j is distance(i, j).
         * \param[in] size The size the graph should have
         * \param[in] distance Binary function taking std::size_t arguments and returning the distance between two points
         */
        explicit CompleteGraph(std::size_t size, std::function<F(std::size_t, std::size_t)> const& distance) : size_(size), distance_(distance) {}

        //! Access to size_
        std::size_t size() const { return size_; }

        //! Access to distance_
        std::function<F(std::size_t, std::size_t)> const& distance() const { return distance_; }

    private:
        //! The size of the graph
        std::size_t size_;

        //! The distance function used to find the distance between point i and point j
        std::function<F(std::size_t, std::size_t)> const& distance_;

        //! Distance function that just returns F(1)
        std::function<F(std::size_t, std::size_t)> returnOne = [] (std::size_t, std::size_t) { return F(1); };
};

//! Weigth map for all edges
template<typename F>
class EdgeWeightMap
{
    public:
        typedef F value_type;
        typedef F reference_type;
        typedef reference_type reference;
        typedef EdgeDescriptor key_type;
        typedef readable_property_map_tag category;

        //! Constructor from a distance function
        explicit EdgeWeightMap(std::function<F(std::size_t, std::size_t)> const& distance) : distance_(distance) {}

        //! Operator to dereference the property map
        value_type operator[](key_type key) const { return distance_(key.first, key.second); }

        //! Get function
        friend inline value_type get(EdgeWeightMap<F> const& edgeWeightMap, EdgeWeightMap<F>::key_type const& key) { return edgeWeightMap[key]; }

    private:
        //! The distance function
        std::function<F(std::size_t, std::size_t)> const& distance_;
};

//! Return the number of vertices of a CompleteGraph
template<typename F>
std::size_t num_vertices(CompleteGraph<F> const& g) { return g.size(); }

//! Return a pair allowing iteration over all vertices
template<typename F>
std::pair<VertexIterator, VertexIterator> vertices(CompleteGraph<F> const& g) { return std::make_pair(VertexIterator(0), VertexIterator(g.size())); }

//! Return a pair allowing iteration over all outgoing edges of a vertex
template<typename F>
std::pair<OutEdgeIterator, OutEdgeIterator> out_edges(VertexDescriptor s, CompleteGraph<F> const& g) { return std::make_pair(OutEdgeIterator(s), OutEdgeIterator(s, g.size())); }

//! Return the out-degree which is constant size - 1 for all vertices
template<typename F>
std::size_t out_degree(VertexDescriptor, CompleteGraph<F> const& g) { return g.size() - 1; }

//! Return the source of an edge
template<typename F>
VertexDescriptor source(EdgeDescriptor e, CompleteGraph<F> const&) { return e.first; }

//! Return the target of an edge
template<typename F>
VertexDescriptor target(EdgeDescriptor e, CompleteGraph<F> const&) { return e.second; }

//! Return the index map
template<typename F>
identity_property_map get(vertex_index_t, CompleteGraph<F> const&) { return identity_property_map(); }

//! Return the distance map
template<typename F>
EdgeWeightMap<F> get(edge_weight_t, CompleteGraph<F> const& g) { return EdgeWeightMap<F>(g.distance()); }

//! Wrapper function for automatic template parameter
template<typename F>
CompleteGraph<F> makeCompleteGraph(std::size_t size, std::function<F(std::size_t, std::size_t)> const& distance) { return CompleteGraph<F>(size, distance); }

//! Compute a metric TSP solution through the points supplied
/*!
 * This function finds a solution through n many points whose pairwise distance is given by a function argument.
 * The supplied distance function needs to satisfy the triangle inequality and must be symmetric.
 * \tparam F The type of the return value of distance
 * \param[in] size The number of points through which the TSP tour should be found
 * \param[in] start The index of the point at which to start
 * \param[in] distance A function taking two std::size_t's and returning the distance between point i and point j
 * \return A vector representing the TSP tour
 */
template<typename F>
std::vector<std::size_t> computeTspTour(std::size_t size, std::size_t start, std::function<F(std::size_t, std::size_t)> const& distance)
{
    std::vector<std::size_t> tour;
    const auto completeGraph = makeCompleteGraph(size, distance);
    metric_tsp_approx_tour_from_vertex(completeGraph, start, std::back_inserter(tour));
    return tour;
}

int main()
{
    typedef std::complex<double> Point;

    const std::vector<Point> points{{.0, .0}, {1.0, 2.0}, {1.0, 5.0}, {2.5, 9.2}, {-100.2, 24.1}, {.1, 10.0}};
    const std::function<double(std::size_t, std::size_t)> distance = [&points] (std::size_t i, std::size_t j) { return std::abs(points[i] - points[j]); };

    const auto tour = computeTspTour(points.size(), 0, distance);

    std::cout << "Found TSP tour:\n";
    std::copy(tour.cbegin(), tour.cend(), std::ostream_iterator<char>(std::cout, " "));

    return EXIT_SUCCESS;
}

I'm also happy if someone has an alternative suggestion that is shorter or avoids creating any graph at all, a complete graph does not really carry any information besides the number of its vertices.

Answer 1

DFS and TSP algorithms require a graph to be both "vertex list" AND "incidence graph" (i.e. a graph with access to vertex neighbors).

Your graph has to have something like

 struct traversal_category
        : public virtual boost::vertex_list_graph_tag
        , public virtual boost::adjacency_graph_tag
        , public virtual boost::incidence_graph_tag
    {
    };

     typedef typename boost::adjacency_iterator_generator<CompleteGraph<F>, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;

instead of

 typedef vertex_list_graph_tag traversal_category;
 typedef void adjacency_iterator;

With these changes plus some cosmetic ones your code passes compilation.

Vertex index map is optional, Boost will wrap your code with VertexMap and ColorMap, likely based on unordered_map. It will be less efficient then "identity" or similar custom maps but will work.

Good luck!

Answer 2

Your code for custom "complete" graph seems OK.

The critical component needed by DFS is "vertex index map": essentially a one-to-one correspondence between vertex_descriptor and int, such that each vertex is mapped to a number in the interval [0, num_vertices(g)). For "standard" graphs such mapping is known, and DFS uses some meta-programming to deduce the type of appropriate ColorMap.

In you case, the vertex_descriptor IS an integer within correct interval and the mapping is "identical map". You only have to express it with code similar to the following:

namespace boost{ 
    template<class F>
    struct property_map< CompleteGraph<F>, vertex_index_t >
    {

        typedef identity_property_map type;

        //or more fancier 
        //typedef CompleteGraph<F> graph_t;
        //typedef typed_identity_property_map<typename graph_t::vertex_descriptor> type;

        typedef type const_type;
    };

    //then you define a "get" function:
    template<class F>
    identity_property_map
      get(vertex_index_t, const CompleteGraph<F>& /*g -- not used */) 
    {
       return identity_property_map();
    }
} //namespace boost

It should be enough. If some algorithm requires other "property_maps" for your graph type, you can define them in a similar manner.

Good luck!