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]]>s*f(n,s) <= z(n, f(n,s), d+1, 2) < sqrt(n*d)*(f(n,s)-1) + n

Assuming that sqrt(n*d)/s 1, we can get a better bound by swapping the order of the arguments:

s*f(n,s) <= z(f(n,s), n, 2, d+1) d (which is true unless the problem is trivial) we can we-arrange to say that f(n,s) <= O(n/s)^(d+1), which matches our bound.

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]]>http://procaccia.info/papers/rent.pdf

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