On the k-independence required by linear probing and minwise independence

  • Authors:
  • Mihai Pătraşcu;Mikkel Thorup

  • Affiliations:
  • AT&bs;AT&bs

  • Venue:
  • ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
  • Year:
  • 2010

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Abstract

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]. For (1 + ε)-approximate minwise independence, we show that Ω(lg 1/ε)-independent hash functions are required, matching an upper bound of [Indyk, SODA'99]. We also show that the multiply-shift scheme of Dietzfelbinger, most commonly used in practice, fails badly in both applications.