### The Power of Simple Tabulation HashingThe Power of Simple Tabulation Hashing

Access Restriction
Subscribed

 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

#### Open content in new tab

Source: ACM Digital Library