Polynomial hash functions are reliable

M. Dietzfelbinger, J. Gil, Y. Matias, N. Pippenger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

79 Scopus citations

Abstract

Polynomial hash functions are well studied and widely used in various applications. They have gained popularity because of certain performances they exhibit. It has been shown that even linear hash functions are expected to have such performances. However, quite often we would like the hash functions to be reliable, meaning that they perform well with high probability; for some certain important properties even higher degree polynomials were not known to be reliable. We show thal, for certain important properties linear hash functions are not reliable. We give indication that quadratic hash functions might not be reliable. On the positive side, we prove that cubic hash functions are reliable. In a more general setting, we show that higher degree of the polynomial hash functions translates into higher reliability. We also introduce a new class of hash functions, which enables to reduce the universe size in an efficient and simple manner. The reliability results and the new class of hash functions are used for some fimdamental applications: improved and simplified reliable algorithms for perfect hash functions and real-time dictionaries, which use significantly less random bits, and tighter upper bound for the program size of perfect hash functions.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 19th International Colloquium, Proceedings
EditorsWerner Kuich
PublisherSpringer Verlag
Pages235-246
Number of pages12
ISBN (Print)9783540557197
DOIs
StatePublished - 1992
Event19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 - Wien, Austria
Duration: 13 Jul 199217 Jul 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume623 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Colloquium on Automata, Languages, and Programming, ICALP 1992
Country/TerritoryAustria
CityWien
Period13/07/9217/07/92

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