c++ - 加权无向图上的 Floyd Warshall(所有对最短路径) - Boost Graph

Question

我在使用 Boost 图中的 Floyd Warshall(所有对最短路径)时遇到了一些问题。有什么方法可以直接向 floyd_warshall_all_pairs_shortest_paths 提供有向加权图吗？似乎它的所有函数重载都需要一些我不完全理解的额外参数。以下是我正在编写的测试代码(它无法编译，因为我对 floyd_warshall_all_pairs_shortest_paths 的调用不完整)

#include <iostream>

#include <map>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/floyd_warshall_shortest.hpp>

typedef boost::property<boost::edge_weight_t, double> EdgeWeightProperty;
typedef boost::adjacency_list<boost::vecS, boost::vecS, 
                              boost::undirectedS, boost::no_property, 
                              EdgeWeightProperty> Graph;
typedef unsigned long t_indx;

int main()
{
  typedef boost::graph_traits<Graph>::vertex_descriptor vertex_des;
  std::map<vertex_des, std::map<vertex_des, int> > matrix;
  Graph sp_graph;

  int edgelet_sp[] = { 1,     2,
                       1,     3,
                       1,     4,
                       2,     5,
                       3,     4,
                       3,     6,
                       4,     5,
                       4,     6,
                       4,     7,
                       5,     7,
                       6,     7 };
  double edgelet_vals[] = {  4,
                            10,
                             3,
                             1,
                            12,
                            20,
                             6,
                             3,
                             0,
                             3,
                             9};
  int num_edges = 11;

  /* make the superpixel graph */
  for (t_indx i = 0; i < num_edges; ++i) {
    add_edge(edgelet_sp[i]-1, edgelet_sp[i+num_edges]-1, edgelet_vals[i], sp_graph);
  }

  std::cout << num_vertices(sp_graph) << std::endl;

  bool floyd2 =
        boost::floyd_warshall_all_pairs_shortest_paths
          (sp_graph, matrix);
  return 0;
}

我是 BGL 的新手，所以非常感谢任何帮助。例如，是否有更优雅的方式来编写此代码(没有 edgelet_sps 和 edgelet_vals 的声明，两者都将被替换)？谢谢。

Answer 1

我想(在互联网的帮助下)我需要使用 boost::get(boost::edge_weight, g) 直接向 floyd warshall 提供无向加权图。下面的代码编译并工作(这里是下面示例的 graph 的图)

#include <iostream>
#include <boost/graph/undirected_graph.hpp>
#include <boost/graph/exterior_property.hpp>
#include <boost/graph/floyd_warshall_shortest.hpp>

// type for weight/distance on each edge
typedef double t_weight;

// define the graph type
typedef boost::property<boost::edge_weight_t, t_weight> EdgeWeightProperty;
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, 
                              boost::no_property, EdgeWeightProperty> Graph;

typedef boost::property_map<Graph, boost::edge_weight_t>::type WeightMap;

// Declare a matrix type and its corresponding property map that
// will contain the distances between each pair of vertices.
typedef boost::exterior_vertex_property<Graph, t_weight> DistanceProperty;
typedef DistanceProperty::matrix_type DistanceMatrix;
typedef DistanceProperty::matrix_map_type DistanceMatrixMap;


int main()
{
  Graph g;

  const int num_edges = 11;

  // define edges
  int edges[] = { 1,     2,
                  1,     3,
                  1,     4,
                  2,     5,
                  3,     4,
                  3,     6,
                  4,     5,
                  4,     6,
                  4,     7,
                  5,     7,
                  6,     7 };

  // define the weight on edges
  t_weight weight[] = {  4,
                        10,
                         3,
                         1,
                        12,
                        20,
                         6,
                         3,
                         0,
                         3,
                         9 };

  // iterate over all edges and insert them in the graph
  for (std::size_t k = 0; k < num_edges; ++k)
    boost::add_edge(edges[k*2]-1, edges[k*2+1]-1, weight[k], g);

  WeightMap weight_pmap = boost::get(boost::edge_weight, g);

  // set the distance matrix to receive the floyd warshall output
  DistanceMatrix distances(num_vertices(g));
  DistanceMatrixMap dm(distances, g);

  // find all pairs shortest paths
  bool valid = floyd_warshall_all_pairs_shortest_paths(g, dm, 
                                            boost::weight_map(weight_pmap));

  // check if there no negative cycles
  if (!valid) {
    std::cerr << "Error - Negative cycle in matrix" << std::endl;
    return -1;
  }

  // print upper triangular part of the distance matrix
  std::cout << "Distance matrix: " << std::endl;
  for (std::size_t i = 0; i < num_vertices(g); ++i) {
    for (std::size_t j = i; j < num_vertices(g); ++j) {
      std::cout << "From vertex " << i+1 << " to " << j+1 << " : ";
      if(distances[i][j] == std::numeric_limits<t_weight>::max())
        std::cout << "inf" << std::endl;
      else
        std::cout << distances[i][j] << std::endl;
    }
    std::cout << std::endl;
  }

  return 0;
}