Open Access
August, 1992 A Limit Theory for Random Skip Lists
Luc Devroye
Ann. Appl. Probab. 2(3): 597-609 (August, 1992). DOI: 10.1214/aoap/1177005651


The skip list was introduced by Pugh in 1989 as a data structure for dictionary operations. Using a binary tree representation of skip lists, we obtain the limit law for the path lengths of the leaves in the skip list. We also show that the height (maximal path length) of a skip list holding $n$ elements is in probability asymptotic to $c \log_{1/p} n$, where $c$ is the unique solution greater than 1 of the equation $\log(1 - p) = \log(c - 1) - \lbrack c/(c - 1) \rbrack \log c$, and $p \in (0, 1)$ is a design parameter of the skip list.


Download Citation

Luc Devroye. "A Limit Theory for Random Skip Lists." Ann. Appl. Probab. 2 (3) 597 - 609, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0754.68039
MathSciNet: MR1177901
Digital Object Identifier: 10.1214/aoap/1177005651

Primary: 68P05
Secondary: 60J85 , 68Q25

Keywords: branching processes , data structures , height of a tree , probabilistic analysis , Skip list , weak convergence

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
Back to Top