Automata, Languages and Programming

Volume 6198 of the series Lecture Notes in Computer Science pp 715-726

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

  • Mihai PǎtraşcuAffiliated withAT&T Labs
  • , Mikkel ThorupAffiliated withAT&T Labs

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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.