BIT Numerical Mathematics

, Volume 32, Issue 2, pp 316–332 | Cite as

Average search and update costs in skip lists

  • Thomas Papadakis
  • J. Ian Munro
  • Patricio V. Poblete
Algorithm Theory

Abstract

Skip lists, introduced by Pugh, provide an alternative to search trees, although a precise analysis of their behaviour had been elusive. The exact value of the expected cost for the search of themth element in a skip list ofn elements is derived first in terms of previously studied functions, and secondly as an asymptotic expression. The latter suggests that Pugh's upper bound of the expected search cost is fairly tight for the interesting cases. Assuming a uniform query distribution, the exact and an asymptotic value of the average (over allm) expected search cost in a skip list ofn elements is also derived. Finally, all insert and delete costs are obtained.

CR classification

E.1 F.2.2 

AMS classification

68E05 

Keywords

skip lists dictionary probabilistic algorithms asymptotic analysis 

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Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • Thomas Papadakis
    • 1
    • 2
  • J. Ian Munro
    • 1
    • 2
  • Patricio V. Poblete
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Departamento de Ciencias de la ComputaciónUniversidad de ChileSantiagoChile

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