21 Jan 2004
CS 3243 - Heuristics
22
Optimality of A* (proof)
nSuppose some suboptimal goal G2 has been generated and is in the fringe. Let n be an unexpanded node in the fringe such that n is on a shortest path to an optimal goal G.
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nf(G2) > f(G) from above
nh(n) ≤ h^*(n) since h is admissible
ng(n) + h(n) ≤ g(n) + h*(n)
nf(n) ≤ f(G)
nHence f(G2) > f(n), and A* will never select G2 for expansion
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