Affiliation:
1. University of Copenhagen, Denmark
Abstract
We show that linear probing requires 5-independent hash functions for expected constant-time performance, matching an upper bound of Pagh et al. [2009]. More precisely, we construct a random 4-independent hash function yielding expected logarithmic search time for certain keys. For (1 + ϵ)-approximate minwise independence, we show that Ω(lg 1/ϵ)-independent hash functions are required, matching an upper bound of Indyk [2001]. We also show that the very fast 2-independent multiply-shift scheme of Dietzfelbinger [1996] fails badly in both applications.
Funder
Danish Council for Independent Research under the Sapere Aude research carrier programme
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
10 articles.
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