Search trees: Metric aspects and strong limit theorems
| Autor: | Rudolf Grübel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
60B99 Wiener index 05C05 FOS: Mathematics Limit (mathematics) Mathematics Discrete mathematics Binary tree Probability (math.PR) metric trees Sorting 68Q25 subtree size metric Metric space Tree (data structure) path length Convergence of random variables Metric (mathematics) 60J10 Doob–Martin compactification vector-valued martingales Statistics Probability and Uncertainty Random variable silhouette Mathematics - Probability |
| Zdroj: | Ann. Appl. Probab. 24, no. 3 (2014), 1269-1297 |
| Popis: | We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree. Published in at http://dx.doi.org/10.1214/13-AAP948 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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