Average time behavior of distributive sorting algorithms |
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Authors: | L Devroye T Klincsek |
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Affiliation: | 1. School of Computer Science, Mc Gill University, Burnside Hall 805, Sherbrooke St. West, H3A 2K6, Montreal, PQ, Canada
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Abstract: | In this paper we investigate the expected complexityE(C) of distributive (“bucket”) sorting algorithms on a sampleX 1, ...,X n drawn from a densityf onR 1. Assuming constant time bucket membership determination and assuming the use of an average timeg(n) algorithm for subsequent sorting within each bucket (whereg is convex,g(n)/n↑∞,g(n)/n 2 is nonincreasing andg is independent off), the following is shown: - Iff has compact support, then ∫g(f(x))dx<∞ if and only ifE(C)=0(n).
- Iff does not have compact support, then \(E(C)/n\xrightarrow{n}\infty \) .
No additional restrictions are put onf. |
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