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Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families (1999)
| Venue: | In Proc. International Workshop on Randomization and Approximation Techniques in Computer Science |
| Citations: | 8 - 0 self |
BibTeX
@INPROCEEDINGS{Saks99lowdiscrepancy,
author = {Michael Saks and Aravind Srinivasan and Shiyu Zhou and David Zuckerman},
title = {Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families},
booktitle = {In Proc. International Workshop on Randomization and Approximation Techniques in Computer Science},
year = {1999},
pages = {29--32},
publisher = {Springer}
}
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Abstract
Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze & Mitzenmacher defined the following notion of ffl-approximate min-wise independent permutation families. A multiset F of permutations of f0; 1; : : : ; n \Gamma 1g is such a family if for all K ` f0; 1; : : : ; n \Gamma 1g and any x 2 K, a permutation chosen uniformly at random from F satisfies j Pr[minf(K)g = (x)] \Gamma 1 jKj j ffl jKj : We show connections of such families with low discrepancy sets for geometric rectangles, and give explicit constructions of such families F of size n O( p log n) for ffl = 1=n \Theta(1) , improving upon the previously best-known bound of Indyk. We also present polynomialsize constructions when the min-wise condition is required only for jKj 2 O(log 2=3 n) , with ffl 2 \GammaO(log 2=3 n) . Keywords: Combinatorial problems; min-wise independent permutations; information retrieval; document filtering; pseudorandom permutations; explicit constructions.
Keyphrases
explicit construction following notion min-wise independent permutation geometric rectangle low discrepancy set present polynomialsize construction jkj ffl jkj combinatorial problem document filtering near-duplicate web document frieze mitzenmacher best-known bound ffl-approximate min-wise independent permutation family pr minf information retrieval min-wise condition
