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
tov
will beG.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 or None to indicate a hidden edge.
- 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
ortarget
is not inG
.- 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 are2*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]