On the joint distribution of the insertion path length and the number of comparisons in search trees
Discrete Applied Mathematics
On convergence rates in the central limit theorems for combinatorial structures
European Journal of Combinatorics
Universal Limit Laws for Depths in Random Trees
SIAM Journal on Computing
A generating functions approach for the analysis of grand averages for multiple QUICKSELECT
proceedings of the eighth international conference on Random structures and algorithms
Phase changes in random m-ary search trees and generalized quicksort
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Analysis of multiple quickselect variants
Theoretical Computer Science
A combinatorial approach to the analysis of bucket recursive trees
Theoretical Computer Science
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In this paper, we show for generalized $M$-ary search trees that the Steiner distance of $p$ randomly chosen nodes in random search trees is asymptotically normally distributed. The special case $p=2$ shows, in particular, that the distribution of the distance between two randomly chosen nodes is asymptotically Gaussian. In the presented generating functions approach, we consider first the size of the ancestor-tree of $p$ randomly chosen nodes. From the obtained Gaussian limiting distribution for this parameter, we deduce the result for the Steiner distance. Since the size of the ancestor-tree is essentially the same as the number of passes in the (generalized) Multiple Quickselect algorithm, the limiting distribution result also holds for this parameter.