- pgr_bdDijkstra - Bidirectional Dijkstra algorithm for the shortest paths.
- pgr_bdDijkstraCost - Proposed - Bidirectional Dijkstra to calculate the cost of the shortest paths
- pgr_bdDijkstraCostMatrix - proposed - Bidirectional Dijkstra algorithm to create a matrix of costs of the shortest paths.

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.

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