Some properties of exponential trees

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
Rafik Aguech, Sudip Bose, H. Mahmoud, Yi Zhang
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引用次数: 1

Abstract

Exponential recursive trees and exponential PORTs are introduced in H. Mahmoud (Profile of random exponential recursive trees. Methodology and Computing in Applied Probability (accepted) 2021). In that reference, the author investigates the order and node profile of these species. Several other equally important properties remain to be explored. The aim of the present manuscript is to establish fundamental properties concerning leaves (and their profile level by level) and distances in these trees. Some results fall back on the order of a tree. For the number of leaves in both flavours, we find (under appropriate scaling for each) a limit distribution uniquely characterized by inductively constructed moments. We find an limit for the scaled total (external) path length in an exponential recursive tree (PORT) in terms of the known distribution of the scaled order given in Mahmoud [11]. These total path lengths are indicative of the depth of a randomly chosen node (external node) in an exponential recursive tree (PORT).
指数树的一些性质
在H. Mahmoud随机指数递归树概要中引入了指数递归树和指数端口。应用概率的方法和计算(已接受)2021)。在该文献中,作者研究了这些物种的顺序和节点分布。其他几个同样重要的性质仍有待探索。本手稿的目的是建立有关树叶的基本性质(及其剖面水平逐级)和距离在这些树。有些结果落回到树的顺序上。对于两种口味的叶子数量,我们发现(在适当的缩放下)一个由归纳构造矩唯一表征的极限分布。我们根据Mahmoud[11]中给出的已知比例阶分布,找到了指数递归树(PORT)中缩放总(外部)路径长度的极限。这些总路径长度表示指数递归树(PORT)中随机选择的节点(外部节点)的深度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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