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Huw: I agree. This paragraph is simply not true. I'm not even sure what <math>O(log(h*(x))</math> even means in this context since <math>x</math> represents a vertex in a graph and <math>O(f(n))</math> should imply that <math>f</math> is the dominant term in the cost of an algorithm when <math>n\rightarrow\infty</math>.
:<math>O(log(h^{*}(x))</math> is the asymptotic growth of the perfect heuristic <math>h^{*}</math>. I explained this and inserted a reference. Btw., stating that visiting each edge and each node once "is linear in the number of vertices and edges" assumes finite graphs. A* can be used for infinite graphs, or at least graphs that do not fit in any computer memory using an "explicit" representation. [[User:Qwertyus|Qwertyus]] 00:44, 21 July 2006 (UTC)
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