21 Jan 2004
CS 3243 - Heuristics
21
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.
n
n
n
n
n
nf(G2)  = g(G2) since h(G2) = 0
ng(G2) > g(G) since G2 is suboptimal
nf(G)   = g(G) since h(G) = 0
nf(G2)  > f(G) from above