On Total Node Path Length and the Silhouette of the Random M-Ary Serach Trees

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Project title

Code/計畫編號

NSC99-2115-M019-001

Translated Name/計畫中文名

m 分支樹狀結構上與節點路徑總數及剪影問題的再分析

Project Coordinator/計畫主持人

Hua-Huai Chern

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Computer Science and Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2125628

Year

2010

Start date/計畫起

01-08-2010

Expected Completion/計畫迄

31-07-2011

Bugetid/研究經費

251千元

ResearchField/研究領域

數學

本次研龛計畫旨在以w分支樹狀結構（m-ary search trees1)傲為再度研龛的主要題材’針對與此結構有閼的兩個間題一由節點(nodes)與根點(root)間的距離總數及所謂的剪影(silhouette)—來進衧分析與研龛。 (nodes) (root) 衧與全間需求量的一併考慮下'對相閼連的兩個量的極限分佈的刻畫與可能存在的相變現象進衧再度地研龛。 (silhouette) 果豐富的側禽或輪廓’ 一種源於對二无搜尋樹利用參數的二无展開式與樹裡路徑的對應下所走義的量'以此結構為主要的分析對象。"The goal of this project is to investigate two problems related to the m-ary search tree structures2 Ôthe limit laws on the total node path lengths and the so-called “silhouette” of a tree. For the aspect of limit laws on the total node path lengths, unlike the way we have used ever, the authors shall deal with this variant and the space requirements simultaneously, then try to derive the limit laws and possible phase changes. In addition, the “silhouette” of a tree that is different from the “profile” that are widely studied among more kinds of trees and is ever newly defined on binary search trees by the relation between the binary expansion of a parameter of real numbers and the associated path in the tree, is a brand new problem to be further studied on the m-ary search trees."

Keyword(s)

$m$-ary 搜尋樹
TKPL
TNPL
漸近遞移
相變
極限律

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On Total Node Path Length and the Silhouette of the Random M-Ary Serach Trees

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