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On The K-independence Required By Linear Probing And Minwise Independence

Thorup Mikkel. Arxiv 2013

[Paper]    
ARXIV Independent

We show that linear probing requires 5-independent hash functions for expected constant-time performance, matching an upper bound of [Pagh et al. STOC’07]. More precisely, we construct a 4-independent hash functions yielding expected logarithmic search time. For (1+{\epsilon})-approximate minwise independence, we show that Ω(log 1/{\epsilon})-independent hash functions are required, matching an upper bound of [Indyk, SODA’99]. We also show that the very fast 2-independent multiply-shift scheme of Dietzfelbinger [STACS’96] fails badly in both applications.

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