## Bidirectional search

Bidirectional search is a graph search algorithm that finds a shortest path from an initial vertex to a goal vertex in a directed graph. It runs two simultaneous searches: one forward from the initial state and one backward from the goal, stopping when the two meet in the middle. The reason for this approach is that in many cases it is faster: for instance, in a simplified model of search problem complexity in which both searches expand a tree with branching factor b, and the distance from start to goal is d, each of the two searches has complexity O(b^{d/2}) (in Big O notation), and the sum of these two search times is much less than the O(b^{d}) complexity that would result from a single search from the beginning to the goal.

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