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Random Records and Cuttings in Binary Search Trees

Published online by Cambridge University Press:  05 March 2010

CECILIA HOLMGREN
CECILIA HOLMGREN*
Affiliation:
Uppsala Universitet, Matematiska Institutionen, Box 480 751 06 Uppsala, Sweden (e-mail: cecilia.holmgren@math.uu.se)
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Abstract

We study the number of random records in a binary search tree with n vertices (or equivalently, the number of cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. The asymptotic distribution of the (normalized) number of records or cuts is found to be weakly 1-stable.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 3 , May 2010 , pp. 391 - 424
Copyright
Copyright © Cambridge University Press 2010

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