Explain a bidirectional search algorithm. What is it?

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A bidirectional search algorithm runs two simultaneous searches. The first go forward from the initial state, and the second goes backward from the goal state. They both meet at a common point, and that’s when the search ends—the goal state links with the initial state in a reverse manner.

A bidirectional search algorithm is a technique used in graph theory and artificial intelligence to find the shortest path between two nodes in a graph. Unlike traditional unidirectional search algorithms like Breadth-First Search (BFS) or Depth-First Search (DFS), which explore the graph starting from a single source node, a bidirectional search explores the graph simultaneously from both the source node and the target node. This approach can be particularly useful in situations where the search space is large, as it can significantly reduce the time complexity compared to unidirectional searches.

Here’s how a bidirectional search algorithm typically works:

  1. Begin with two search frontiers: one starting from the source node and another starting from the target node.
  2. Expand the search in both directions simultaneously, alternating between expanding nodes in the forward direction (from the source node) and nodes in the backward direction (from the target node).
  3. At each step, check if any node being expanded in one direction is also reached by the search from the other direction. If so, a path between the source and target nodes has been found.
  4. Continue the search until either a path is found or both search frontiers have explored all reachable nodes without finding a common intersection.

By exploring the graph from both ends, a bidirectional search algorithm can potentially reduce the search space and improve efficiency, especially in scenarios where the branching factor of the graph is high or the distance between the source and target nodes is large. However, bidirectional search algorithms require additional bookkeeping to track nodes visited from both directions and to manage communication between the two search frontiers. Additionally, they may not always be applicable or beneficial depending on the specific characteristics of the problem and the graph structure.