# pgRouting Manual (3.1)

## 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.

Previous versions of this page

- Supported versions: current(3.1) 3.0 2.6

- Unsupported versions: 2.5

## 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

## See Also

Indices and tables

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