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.
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This research was supported in part by the Natural Science and Engineering Research Council of Canada under grant No. A-8237, the Information Technology Research Centre of Ontario, and FON-DECYT (Chile) under grant 91-1252.
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Papadakis, T., Ian Munro, J. & Poblete, P.V. Average search and update costs in skip lists. BIT 32, 316–332 (1992). https://doi.org/10.1007/BF01994884