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On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications

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1 Author(s)
Siegel, A. ; Dept. of Comput. Sci., Stanford Univ., CA, USA

A mechanism is provided for constructing log-n-wise-independent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed ε<1, a table of nε random words can be accessed by a small O(1)-time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all practical purposes, is also given. A lower bound shows that such a program must take Ω(k /ε) time, and a probabilistic arguments shows that programs can run in O(k22) time. An immediate consequence of these constructions is that double hashing using these universal functions has (constant factor) optimal performance in time, for suitably moderate loads. Another consequence is that a T-time PRAM algorithm for n log n processors (and nk memory) can be emulated on an n-processor machine interconnected by an n×log n Omega network with a multiplicative penalty for total work that, with high probability, is only O(1)

Published in:

Foundations of Computer Science, 1989., 30th Annual Symposium on

Date of Conference:

30 Oct-1 Nov 1989