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

is admissible iff for all nodesf(n) = g(n) + h(n)

* A ^{*} * expands the fringe of the search in contours of increasing

In practice, one might sacrifice admissibility to have a more powerful heuristic function and reduce search time.