Random records and cuttings in binary search trees

Authors:
Cecilia Holmgren
Affiliations:
Uppsala universitet, matematiska institutionen, box 480 751 06 uppsala, sweden (e-mail: cecilia.holmgren@math.uu.se)
Venue:
Combinatorics, Probability and Computing
Year:
2010

Citing 6
Cited 0

A note on the height of binary search trees

Journal of the ACM (JACM)
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
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The art of computer programming, volume 3: (2nd ed.) sorting and searching
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Journal of Algorithms - Analysis of algorithms
Random cutting and records in deterministic and random trees

Random Structures & Algorithms
A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree

Random Structures & Algorithms

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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.