| Optimality
of A* (proof) |
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| n | Suppose
some suboptimal goal G2 has been generated
and is in the |
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| fringe. Let n
be an unexpanded node in the fringe such that n is on |
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| a shortest path
to an optimal goal G. |
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| n | f(G2)¡¡¡¡ > f(G) ¡¡¡¡¡¡ from above |
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| n | h(n)¡¡¡¡ ¡Ü h^*(n)¡¡¡¡ since h
is admissible |
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| n | g(n) +
h(n)¡¡ ¡Ü g(n) + h*(n) |
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| n | f(n) ¡¡¡¡ ¡Ü f(G) |
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| Hence f(G2)
> f(n), and A* will never select G2 for
expansion |
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