A limit theory for random skip lists. (English) Zbl 0754.68039

Summary: The skip list was introduced by W. Pugh [Lect. Notes Comput. Sci. 382, Springer, Berlin, 437-449 (1989)] 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 \(\log(1- p)=\log(c-1)-[c/(c-1)]\log c\), and \(p\in(0,1)\) is a design parameter of the skip list.


68P05 Data structures
68Q25 Analysis of algorithms and problem complexity
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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