Linear Probing with Constant Independence

Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well. Unfortunately, previous analysis rely either on complicated and space...

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Bibliographic Details
Main Authors Pagh, Anna, Pagh, Rasmus, Ruzic, Milan
Format Journal Article
LanguageEnglish
Published 08.12.2006
Subjects
Computer Science - Data Structures and Algorithms
Computer Science - Databases
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Summary:Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well. Unfortunately, previous analysis rely either on complicated and space consuming hash functions, or on the unrealistic assumption of free access to a truly random hash function. Already Carter and Wegman, in their seminal paper on universal hashing, raised the question of extending their analysis to linear probing. However, we show in this paper that linear probing using a pairwise independent family may have expected {\em logarithmic} cost per operation. On the positive side, we show that 5-wise independence is enough to ensure constant expected time per operation. This resolves the question of finding a space and time efficient hash function that provably ensures good performance for linear probing.
DOI:10.48550/arxiv.cs/0612055