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The Maximum Displacement for Linear Probing Hashing

Published online by Cambridge University Press:  24 January 2013

NICLAS PETERSSON
NICLAS PETERSSON*
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: niclas.petersson@gmail.com)
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Abstract

In this paper we study the maximum displacement for linear probing hashing. We use the standard probabilistic model together with the insertion policy known as First-Come-(First-Served). The results are of asymptotic nature and focus on dense hash tables. That is, the number of occupied cells n and the size of the hash table m tend to infinity with ratio n/m → 1. We present distributions and moments for the size of the maximum displacement, as well as for the number of items with displacement larger than some critical value. This is done via process convergence of the (appropriately normalized) length of the largest block of consecutive occupied cells, when the total number of occupied cells n varies.

Keywords

Primary 68W40Secondary 08P1060F0560C05

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 3 , May 2013 , pp. 455 - 476
Copyright
Copyright © Cambridge University Press 2013

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