# 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.

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## Synopsis¶

Based on Dijkstra’s algorithm, the bidirectional search finds a shortest path
a starting vertex (`start_vid`

) to an ending vertex (`end_vid`

).
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.

Values are returned when there is a path.

When the starting vertex and ending vertex are the same, there is no path.

The agg_cost the non included values (v, v) is 0

When the starting vertex and ending vertex are the different and there is no path:

The agg_cost the non included values (u, v) is \(\infty\)

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