Recursive n-gram hashing is pairwise independent, at best

Details Recursive n-gram hashing is pairwise independent, at best Recursive n-gram hashing is pairwise independent, at best

2007-05-31

arxiv.org/abs/0705.4676v7

Daniel Lemire and Owen Kaser, Recursive n-gram hashing is pairwise independent, at best, Computer Speech & Language 24(4): 698

Computer Science

Databases

See software at http://code.google.com/p/ngramhashing/. arXiv admin note: substantial text overlap with arXiv:cs/0610010v3

Scientific paper

10.1016/j.csl.2009.12.001

Many applications use sequences of n consecutive symbols (n-grams). Hashing these n-grams can be a performance bottleneck. For more speed, recursive hash families compute hash values by updating previous values. We prove that recursive hash families cannot be more than pairwise independent. While hashing by irreducible polynomials is pairwise independent, our implementations either run in time O(n) or use an exponential amount of memory. As a more scalable alternative, we make hashing by cyclic polynomials pairwise independent by ignoring n-1 bits. Experimentally, we show that hashing by cyclic polynomials is is twice as fast as hashing by irreducible polynomials. We also show that randomized Karp-Rabin hash families are not pairwise independent.

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