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**Average search and update costs in skip lists.**
*(English)*
Zbl 0761.68030

Summary: Skip lists, introduced by W. Pugh [Skip lists: a probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668-676 (1990); A skip list cook bound. Technical Report CS–TR–2286, Department of Computer Science, University of Maryland/College Park (1989)], 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 the \(m\)th element in a skip list of \(n\) 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 all \(m\)) expected search cost in a skip list on \(n\) elements is also derived. Finally, all insert and delete costs are obtained.

### MSC:

68P05 | Data structures |

Full Text:
DOI

### References:

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