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Hashing with Linear Probing under Nonuniform Probabilities

Published online by Cambridge University Press:  27 July 2009

David Aldous
David Aldous
Affiliation:
Department of StatisticsUniversity of California, Berkeley Berkeley, California 94720
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Abstract

Probabilistic analyses of hashing algorithms usually assume that hash values are uniformly distributed over addresses. We study how one of the simplest schemes, hashing with linear probing, behaves in the nonuniform case. A simple measure μ of nonuniformity is the probability two keys hash to the same address, divided by this probability in the uniform case. It turns out that the effect of nonuniformity is to multiply mean search lengths by μ. For high loads, the longest search is multiplied by approximately μ also. Our theoretical results are asymptotics: simulations show good fits with predictions for mean search lengths, but bad fits for longest search lengths.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988, pp. 1 - 14
Copyright
Copyright © Cambridge University Press 1988

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