A search algorithm is admissible if it always finds an optimal solution path if a solution path exists.
It can be shown[Nilsson, Principles of Artificial Intelligence, Morgan Kaufmann Publishers, 1980.] that the ordered search algorithm, using the heuristic function
f(n) = g(n) + h(n)is admissible iff for all nodes n , h(n) &le h*(n) , where h*(n) is the actual cost of getting from node n to a nearest goal. That is, h(n) must be non-over-estimating; heuristic search with such an h(n) is called A* .
A* expands the fringe of the search in contours of increasing f values until a goal is reached. A* is the most efficient admissible graph search possible, in terms of number of nodes examined for a given h(n) .
In practice, one might sacrifice admissibility to have a more powerful heuristic function and reduce search time.