bidirectional_dijkstra#

bidirectional_dijkstra(G, source, target, weight='weight')[source]#

Dijkstra’s algorithm for shortest paths using bidirectional search.

Parameters:

GNetworkX graph

sourcenode

Starting node.

targetnode

Ending node.

weightstring or function

If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining u to v will be G.edges[u, v][weight]). If no such edge attribute exists, the weight of the edge is assumed to be one.

If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.

Returns:

length, pathnumber and list: length is the distance from source to target. path is a list of nodes on a path from source to target.

Raises:

NodeNotFound: If either source or target is not in G.
NetworkXNoPath: If no path exists between source and target.

See also

shortest_path
shortest_path_length

Notes

Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

The weight function can be used to hide edges by returning None. So weight = lambda u, v, d: 1 if d['color']=="red" else None will find the shortest red path.

In practice bidirectional Dijkstra is much more than twice as fast as ordinary Dijkstra.

Ordinary Dijkstra expands nodes in a sphere-like manner from the source. The radius of this sphere will eventually be the length of the shortest path. Bidirectional Dijkstra will expand nodes from both the source and the target, making two spheres of half this radius. Volume of the first sphere is pi*r*r while the others are 2*pi*r/2*r/2, making up half the volume.

This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems).

Examples

>>> G = nx.path_graph(5)
>>> length, path = nx.bidirectional_dijkstra(G, 0, 4)
>>> print(length)
4
>>> print(path)
[0, 1, 2, 3, 4]