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On Universal Classes of Extremely Random Constant Time Hash Functions and Their Time-Space Tradeoff
| Citations: | 40 - 0 self |
BibTeX
@MISC{Siegel_onuniversal,
author = {Alan Siegel},
title = {On Universal Classes of Extremely Random Constant Time Hash Functions and Their Time-Space Tradeoff},
year = {}
}
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Abstract
A family of functions F that map [0; n] 7! [0; n], is said to be h-wise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl -wise independent functions, ffl ! 1, that can be evaluated in constant time for the standard random access model of computation. Simple extensions give comparable behavior for larger domains. As a consequence, many probabilistic algorithms can for the first time be shown to achieve their expected asymptotic performance for a feasible model of computation. This paper also establishes a tight tradeoff in the number of random seeds that must be precomputed for a random function that runs in time T and is h-wise independent. Categories and Subject Descriptors: E.2 [Data Storage Representation]: Hash-table representation; F.1.2 [Modes of Computation]: Probabilistic Computation; F2.3 [Tradepffs among Computational Measures]...
Keyphrases
universal class time-space tradeoff constant time computational measure simple extension asymptotic performance many probabilistic algorithm probabilistic computation first time random function standard random access model random seed subject descriptor hash-table representation comparable behavior feasible model tight tradeoff explicit randomized construction independent function data storage representation
