Description
A* uses a best-first search and finds a least-cost path from a given initial node to one goal node (out of one or more possible goals). As A* traverses the graph, it follows a path of the lowest known heuristic cost, keeping a sorted priority queue of alternate path segments along the way.
It uses a distance-plus-cost heuristic function of node (usually denoted ) to determine the order in which the search visits nodes in the tree. The distance-plus-cost heuristic is a sum of two functions:
- the path-cost function, which is the cost from the starting node to the current node (usually denoted )
- an admissible "heuristic estimate" of the distance from to the goal (usually denoted ).
The part of the function must be an admissible heuristic; that is, it must not overestimate the distance to the goal. Thus, for an application like routing, might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points or nodes.
If the heuristic h satisfies the additional condition for every edge x, y of the graph (where d denotes the length of that edge), then h is called monotone, or consistent. In such a case, A* can be implemented more efficiently—roughly speaking, no node needs to be processed more than once (see closed set below)—and A* is equivalent to running Dijkstra's algorithm with the reduced cost .
Read more about this topic: A* Search Algorithm
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