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A* could fail even though using an admissible heuristic estimate
This is an example of a graph that A* will fail to find the shortest path for, if the heuristics looks like that in the image (admissible though not consistent) and a closed set of nodes is used.
Just because using an admissible heuristic estimate in the A* algorithm, it doesn't mean that it will find an optimal path. To the right is a counterexample. --Kri (talk) 02:09, 7 November 2009 (UTC)
Oh, just realized that a closed set cannot be used if the heuristic is not consistent. My image supposes that a closed set is used, and that the heuristic looks like it does (not consistent), which is not allowed. --Kri (talk) 11:12, 21 November 2009 (UTC)