C++ Boost

dijkstra_shortest_paths

Graphs: directed and undirected
Properties: color, distance, weight, vertex index
Complexity: O((V + E) log V)
Where Defined: boost/graph/dijkstra_shortest_paths.hpp

(1)
template <class VertexListGraph>
void
dijkstra_shortest_paths(VertexListGraph& g,
  typename graph_traits<VertexListGraph>::vertex_descriptor s);

(2)
template <class VertexListGraph, class DistanceMap>
void
dijkstra_shortest_paths(VertexListGraph& g,
  typename graph_traits<VertexListGraph>::vertex_descriptor s, 
  DistanceMap d);

(3)
template <class VertexListGraph, class DistanceMap, class UniformCostVisitor>
void
dijkstra_shortest_paths(VertexListGraph& g, 
  typename graph_traits<VertexListGraph>::vertex_descriptor s, 
  DistanceMap d, UniformCostVisitor visit);

(4)
template <class VertexListGraph, class UniformCostVisitor, 
          class DistanceMap, class WeightMap, class ColorMap, class VertexIndexMap>
void
dijkstra_shortest_paths(VertexListGraph& g,
  typename graph_traits<VertexListGraph>::vertex_descriptor s, 
  DistanceMap distance, WeightMap weight, ColorMap color, VertexIndexMap id,
  UniformCostVisitor vis);

This is the modified Dijkstra algorithm [10,8] which solves the single-source shortest-paths problem on a weighted, directed graph for the case where all edge weights are nonnegative. See Section Shortest-Paths Algorithms for some background to the shortest-path problem. The priority queue used inside the algorithm is implemented with a heap for efficiency.

There are four versions of the algorithm to accommodate whether the necessary graph properties will be supplied by the graph object or externally via a argument to this function. The properties needed by the algorithm are distance, weight, color, and vertex index. Version 3 and 4 of the algorithm also include a visitor argument for added extensibility.

Requirements on Types

Complexity

The time complexity is O((V + E) log V), or just O(E log V) if all vertices are reachable from the source.

Example

The source code for this example is in examples/dijkstra.cpp.

int 
main(int , char* [])
{
  using namespace boost;

  typedef property<edge_weight_t, int> weightp;
  typedef adjacency_list< listS, vecS, directedS, 
    property<vertex_color_t,default_color_type>, weightp > Graph;
  typedef graph_traits<Graph>::vertex_descriptor Vertex;

  typedef std::pair<int,int> E;

  const int num_nodes = 5;
  E edges[] = { E(0,2), 
                E(1,1), E(1,3), E(1,4),
                E(2,1), E(2,3), 
                E(3,4),
                E(4,0), E(4,1) };
  int weights[] = { 1, 2, 1, 2, 7, 3, 1, 1, 1};

  Graph G(num_nodes, edges, edges + sizeof(edges)/sizeof(E), weights);

  std::vector<Vertex> p(num_vertices(G));
  std::vector<int> d(num_vertices(G));

  Vertex s = *(vertices(G).first);
  p[s] = s;  
  dijkstra_shortest_paths(G, s, &d[0], 
    make_ucs_visitor(record_predecessors(&p[0], on_edge_relaxed())));

  std::cout << "distances from start vertex:" << std::endl;
  graph_traits<Graph>::vertex_iterator vi, vend;
  for(tie(vi,vend) = vertices(G); vi != vend; ++vi)
    std::cout << "distance(" << *vi << ") = " << d[*vi] << std::endl;
  std::cout << std::endl;

  std::cout << "shortest paths tree" << std::endl;
  adjacency_list<> tree(num_nodes);
  
  for(tie(vi,vend) = vertices(G); vi != vend; ++vi)
    if (*vi != p[*vi])
      add_edge(p[*vi], *vi, tree);

  print_graph(tree);

  return 0;
}
The output is:
  distances from start vertex:
  distance(0) = 0
  distance(1) = 6
  distance(2) = 1
  distance(3) = 4
  distance(4) = 5

  shortest paths tree
  0 --> 2 
  1 --> 
  2 --> 3 
  3 --> 4 
  4 --> 1 


Copyright © 2000 Jeremy Siek, Univ.of Notre Dame (jsiek@lsc.nd.edu)