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Bidirectional Dijkstra - Family of functions¶
- pgr_bdDijkstra - Bidirectional Dijkstra algorithm for the shortest paths.
- pgr_bdDijkstraCost - Bidirectional Dijkstra to calculate the cost of the shortest paths
- pgr_bdDijkstraCostMatrix - Bidirectional Dijkstra algorithm to create a matrix of costs of the shortest paths.
Synopsis¶
Based on Dijkstra’s algorithm, the bidirectional search finds a shortest path a starting vertex to an ending vertex.
It runs two simultaneous searches: one forward from the source, and one backward from the target, stopping when the two meet in the middle.
This implementation can be used with a directed graph and an undirected graph.
Characteristics¶
The main Characteristics are:
- Process is done only on edges with positive costs.
- A negative value on a cost column is interpreted as the edge does not exist.
- Values are returned when there is a path.
- When there is no path:
- When the starting vertex and ending vertex are the same.
- The aggregate cost of the non included values \((v, v)\) is \(0\)
- When the starting vertex and ending vertex are the different and there is
no path:
- The aggregate cost the non included values \((u, v)\) is \(\infty\)
- When the starting vertex and ending vertex are the same.
- For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.
- Running time (worse case scenario): \(O((V \log V + E))\)
- For large graphs where there is a path bewtween the starting vertex and ending
vertex:
- It is expected to terminate faster than pgr_dijkstra