johnson_all_pairs_shortest_paths

// named parameter version
template <typename Graph, typename DistanceMatrix, typename P, typename T, typename R>
bool johnson_all_pairs_shortest_paths(Graph& g, DistanceMatrix& D,
  const bgl_named_params<P, T, R>& params = all defaults)

// non-named parameter version
template <typename Graph, typename DistanceMatrix,
          typename VertexIndex, typename WeightMap, typename DT>
bool
johnson_all_pairs_shortest_paths(VertexAndEdgeListGraph& g1, 
  DistanceMatrix& D,
  VertexIndex i_map, WeightMap w_map, DT zero)

This algorithm should be used to compute shortest paths between every pair of vertices for sparse graphs. For dense graphs, use floyd_warshall_all_pairs_shortest_paths.

Where Defined

boost/graph/johnson_all_pairs_shortest.hpp

Parameters

A directed or undirected graph. The graph type must be a model of Vertex List Graph, Edge List Graph, and Incidence Graph.

The length of the shortest path between each pair of vertices u,v in the graph is stored in D[u][v]. The set of types {DistanceMatrix, vertices_size_type, D} must be a model of BasicMatrix where D is the value type of the DistanceMap.

Named Parameters

The weight or ``length'' of each edge in the graph. The type WeightMap must be a model of Readable Property Map. The edge descriptor type of the graph needs to be usable as the key type for the weight map. The value type for the map must be Addable with the value type of the distance map.
Default: get(edge_weight, g)

This parameter is no longer needed, and will be ignored.

This maps each vertex to an integer in the range [0, num_vertices(g)). This is necessary for efficient updates of the heap data structure in the internal call to Dijkstra's algorithm. The type VertexIndexMap must be a model of Readable Property Map. The value type of the map must be an integer type. The vertex descriptor type of the graph needs to be usable as the key type of the map.
Default: get(vertex_index, g)

This parameter is no longer needed, and will be ignored.

This function is use to compare distances to determine which vertex is closer to the source vertex. The CompareFunction type must be a model of \stlconcept{BinaryPredicate} and have argument types that match the value type of the WeightMap property map.
Default: std::less<DT> with DT=typename property_traits<WeightMap>::value_type

This function is used to combine distances to compute the distance of a path. The CombineFunction type must be a model of Binary Function. The first argument type of the binary function must match the value type of the DistanceMap property map and the second argument type must match the value type of the WeightMap property map. The result type must be the same type as the distance value type.
Default: std::plus<DT> with DT=typename property_traits<WeightMap>::value_type

This value is used to initialize the distance for each vertex before the start of the algorithm. The type DT must be the value type of the WeigthMap.
Default: std::numeric_limits::max()

This value is used to initialize the distance for the source vertex before the start of the algorithm. The type DT must be the value type of the WeigthMap.
Default: 0

This is used during the execution of the algorithm to mark the vertices. The vertices start out white and become gray when they are inserted in the queue. They then turn black when they are removed from the queue. At the end of the algorithm, vertices reachable from the source vertex will have been colored black. All other vertices will still be white. The type ColorMap must be a model of Read/Write Property Map. A vertex descriptor must be usable as the key type of the map, and the value type of the map must be a model of Color Value.
Default: an iterator_property_map created from a std::vector of default_color_type of size num_vertices(g) and using the i_map for the index map.

Complexity

Example

The file example/johnson-eg.cpp applies Johnson's algorithm for all-pairs shortest paths to the example graph from page 568 of the CLR [8].