An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state.
A* algorithm (pronounced ``A-star'') an algorithm for heuristic search, using an admissible heuristic function f(n) = g(n) + h(n), where g(n) is the known cost to reach node n from the start, and h(n) is the estimated cost from node n to a goal.
The classic algorithm for finding shortests paths given an admissible heuristic. We'll deal with the notion of admissibility (summary: admissible = optimistic). We show how you can prove properties of A*. We'll also briefly discuss IDA* (iterative deepening A*). ...
(**) This should never happen if you have an monotone admissible heuristic. However in games we often have inadmissible heuristics.
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In addition, an admissible heuristic function such as the cost of the minimum spanning tree of the remaining unvisited cities, can be added to the cost so far of a partial tour to increase the amount of prunin.
See also: What is the meaning of Algorithm, Bidirectional search, Search algorithm, System, AI?