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Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger
Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger
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Define f on the integers n > 1 by the recurrence f(n) = min( n, minm|n( 2f(m) + 3f(n/m) ). The function f has f(n) = n as its upper envelope, attained for all prime n.
The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) ~ C(log n)1 + 1/γ for certain constants γ and C, in the sense that for any ε > 0, the inequality f(n) ≤ (C + ε)(log n)1 + 1/γ holds for infinitely many n, while f(n) ≤ (C + ε)(log …