On the k-Independence Required by Linear Probing and Minwise Independence

  • Mihai Pǎtraşcu
  • Mikkel Thorup
Conference paper

DOI: 10.1007/978-3-642-14165-2_60

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)
Cite this paper as:
Pǎtraşcu M., Thorup M. (2010) On the k-Independence Required by Linear Probing and Minwise Independence. In: Abramsky S., Gavoille C., Kirchner C., Meyer auf der Heide F., Spirakis P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg

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 \(\Omega(\lg \frac{1}{\varepsilon})\)-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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mihai Pǎtraşcu
    • 1
  • Mikkel Thorup
    • 1
  1. 1.AT&T Labs 

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