2004/05/01 by Alois Panholzer, Helmut Prodinger
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #math.PR #msc:05C05 #msc:60C05 #msc:60F05 #msc:68P05
paper · pdf · doi:10.1214/105051604000000071
published as Annals of Applied Probability 2004, Vol. 14, No. 2, 718-733
openalex publication_date 2004/05/01 · arxiv created 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal distribution. The special case p=2 reproves the recent result (obtained by the contraction method by Mahmoud and Neininger [Ann. Appl. Probab. 13 (2003) 253–276]), that the distribution of distances in random binary search trees has a Gaussian limit law. In the proof we use the fact that the spanning tree size is closely related to the number of passes in Multiple Quickselect. This parameter, in particular, its first two moments, was studied earlier by Panholzer and Prodinger [Random Structures Algorithms 13 (1998) 189–209]. Here we show also that this normalized parameter has for fixed p-order statistics a Gaussian limit law. For p=1 this gives the well-known result that the depth of a randomly selected node in a random binary search tree converges in law to the Normal distribution.