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

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 epsilon <1, a table of n/sup epsilon / 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 Omega (k/ epsilon ) time, and a probabilistic arguments shows that programs can run in O(k/sup 2// epsilon /sup 2/) 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 n/sup k/ 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).<
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