Abstract
The skip list is a recently introduced data structure that may be seen as an alternative to (digital) tries. In the present paper we analyze the path length of random skip lists asymptotically, i.e. we study the cumulated successful search costs. In particular we derive a precise asymptotic result on the variance, being of ordern 2 (which is in contrast to tries under the symmetric Bernoulli model, where it is only of ordern). We also intend to present some sort of technical toolkit for the skilful manipulation and asymptotic evaluation of generating functions that appear in this context.
Similar content being viewed by others
References
Devroye, L.: A limit theory for random skip lists. Ann. Appl. Probab2, 597–609 (1992)
Flajolet, P., Richmond, L.B.: Generalized digital trees and their difference-differential equations. Random Structures and Algorithms3, 305–320 (1992)
Flajolet, P., Sedgewick, R.: Digital search trees revisited. SIAM J. Comput15, 748–767 (1986)
Flajolet, P., Vitter, J.: Average-case analysis of algorithms and data structures. Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, pp. 431–542. Amsterdam: North-Holland 1990
Kirschenhofer, P., Prodinger, H.: A result in order statistics related to probabilistic counting. (Submitted, 1992)
Kirschenhofer, P., Prodinger, H., Schoißengeier, J.: Zur Auswertung gewisser numerischer Reihen mit Hilfe modularer Funktionen. In: Hlawka, E. (ed.), Zahlentheoretische Analysis II (Lect. Notes Math.1262, 108–110) Berlin, Heidelberg, New York: Springer 1987
Kirschenhofer, P., Prodinger, H., Szpankowski, W.: On the variance of the external pathlength in a symmetric digital trie. Discrete Appl. Math.25, 129–143 (1989)
Kirschenhofer, P., Prodinger, H., Szpankowski, W.: On the balance property of Patricia tries: external pathlength view. Theor. Comput. Sci.68, 1–17 (1989)
Kirschenhofer, P., Prodinger, H., Szpankowski, W.: Digital search trees again revisited: the internal path length perspective. SIAM J. Comput. (to appear)
Kirschenhofer, P., Prodinger, H., Tichy, R.F.: A contribution to the analysis of in situ permutation. Glasnik Mathematicki22(42), 267–278 (1987)
Knuth, D.E.: The art of computer programming, vol. 1, Reading, MA: Addison-Wesley 1968
Knuth, D.E.: The art of computer programming, vol. 3. Reading, MA: Addison-Wesley 1973
Papadakis, T., Munro I., Poblete, P.: Average search and update costs in skip lists. BIT32, 316–332 (1992)
Prodinger, H.: Combinatorics of geometrically distributed random variables: Left-to-right maxima. (Submitted 1992)
Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Commun. ACM33, 668–676 (1990)
Sedgewick, R.: Mathematical analysis of combinatorial algorithms. In: Louchard, G., Latouche, G. (eds.), Probability Theory and Computer Science, pp. 125–205. New York: Academic Press 1983
Szpankowski, W., Rego, V.: Yet another application of a binomial recurrence: order statistics. Computing43, 401–410 (1990)
Whittaker, E.T., Watson, G.N.: A course in modern analysis. Cambridge: Cambridge University Press 1927
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kirschenhofer, P., Prodinger, H. The path length of random skip lists. Acta Informatica 31, 775–792 (1994). https://doi.org/10.1007/BF01178735
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01178735