c++ - boost::graph 中的 ColorMap 用于 metric_tsp_approx 的隐式图

Question

我正在尝试完成以下任务:有一个函数 computeTspTour(size, start, distance) 可以让我得到从 start 开始通过 size 许多顶点的最短路径的近似值。这里，distance 是一个函数对象，它接受两个索引并返回它们之间的距离。

我想利用 boost::graph 的 metric_tsp_approx。为此，我需要一个完整的基数图 size，因此我想为此使用一个隐式定义的图，以避免创建无用的琐碎的巨大图结构。

一切似乎都工作正常，但我的问题是 metric_tsp_approx 在某些时候使用 dijkstra_shortest_paths，它定义了一个 ColorMap。这会导致以下两个问题:

/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;
                                 ^

但是，我不知道如何从我所在的地方修复 ColorMap 的特征，我自己创建颜色属性映射没有任何好处。

我用来创建隐式图并在其上运行 tsp_metric_approx 的代码如下。对于它的长度，我深表歉意，我希望它是直截了当的。它所做的是建立一个类 CompleteGraph，具有一个模板参数 F，用于指定 distance 函数的返回类型。此类具有成为 VertexListGraph 和 IncidenceGraph 所需的迭代器，因此 tsp_metric_approx 可以在其上运行。

#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;
}

如果有人有更短的替代建议或根本避免创建任何图，我也很高兴，一个完整的图除了顶点数之外实际上没有任何信息。

Answer 1

DFS 和 TSP 算法要求图既是“顶点列表”又是“关联图”(即可以访问顶点邻居的图)。

你的图表必须有类似的东西

 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;

代替

 typedef vertex_list_graph_tag traversal_category;
 typedef void adjacency_iterator;

通过这些更改以及一些修饰性更改，您的代码可以通过编译。

顶点索引映射是可选的，Boost 将使用 VertexMap 和 ColorMap 包装您的代码，可能基于 unordered_map。它的效率会低于“身份”或类似的自定义 map ，但会起作用。

祝你好运!