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Author Ptracu, Mihai ♦ Thorup, Mikkel
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2012
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Hashing ♦ Tabulation
Abstract Randomized algorithms are often enjoyed for their simplicity, but the hash functions used to yield the desired theoretical guarantees are often neither simple nor practical. Here we show that the simplest possible tabulation hashing provides unexpectedly strong guarantees. The scheme itself dates back to Zobrist in 1970 who used it for game playing programs. Keys are viewed as consisting of $\textit{c}$ characters. We initialize $\textit{c}$ tables $\textit{H}1,$ ..., $\textit{H}\textit{c}$ mapping characters to random hash codes. A key $x = (x_{1},$ ..., $\textit{x}\textit{c})$ is hashed to $\textit{H}1[\textit{x}1] ⊕ ⋯ ⊕ \textit{H}\textit{c}[\textit{x}\textit{c}],$ where ⊕ denotes bit-wise exclusive-or. While this scheme is not even 4-independent, we show that it provides many of the guarantees that are normally obtained via higher independence, for example, Chernoff-type concentration, min-wise hashing for estimating set intersection, and cuckoo hashing.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2012-06-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 59
Issue Number 3
Page Count 50
Starting Page 1
Ending Page 50

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Source: ACM Digital Library