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The A* Algorithm is the optimal (provided the heuristic function is underestimated), complete & admissible (provided some conditions). I know the proofs of admissibility & optimality.

But how do you prove that the A* Algorithm is complete?

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interesting factoid if the heuristic function is set to h(x)=0 you get dijkstra –  ratchet freak Mar 17 '13 at 17:32
    
yeah, it is. +1 to the point. Thanks. –  vintesh Mar 17 '13 at 18:17
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up vote 6 down vote accepted

For a proof of completeness, it is not necessary to look specificially at A*. Any finite graph search algorithm using a node queue where you take one element off, generate all children of that graph node and put them back into the queue is complete, "A*" is just a special case of that kind of algorithms.

Once you got this, it is easy to find a proof of completeness for arbitary graph search by Google, for example, this one:

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-410-principles-of-autonomy-and-decision-making-fall-2010/lecture-notes/MIT16_410F10_lec04.pdf

The proof itself is not very complex, but IMHO still too long for summarizing it here.

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Thanks. Got the concept. Working on the link provided. –  vintesh Mar 17 '13 at 18:08
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