On a relationship between 2-3 brother trees and dense ternary trees

Olivié, Hendrik

doi:10.1080/00207168008803209

Cited by 3 publications

(1 citation statement)

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“…(See [7] for a further explanation of the relationship between 2-3 brother trees and dense ternary trees.) The class of B-trees of order m is not contained in any class of dense m-ary trees, and vice versa.…”

Section: Basic Definitions and Static Structure Of Dense Multiway Treesmentioning

confidence: 98%

Dense multiway trees

Čulík

Ottmann

Wood

1981

ACM Trans. Database Syst.

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B-trees of order m are a "balanced" class of m-ary trees, which have applications in the areas of fide organization. In fact, they have been the only choice when balanced multiway trees are required. Although they have very simple insertion and deletion algorithms, their storage utilization, that is, the number of keys per page or node, is at worst 50 percent. In the present paper we investigate a new class of balanced may trees, the dense multiway trees, and compare their storage utilization with that of B-trees of order m.Surprisingly, we are able to demonstrate that weakly dense multiway trees have an O(log, N) insertion algorithm. We also show that inserting mh -1 keys in ascending order into an initially empty dense multiway tree yields the complete m-ary tree of height h, and that at intermediate steps in the insertion sequence the intermediate trees can also be considered to be as dense as possible. Furthermore, an analysis of the limiting dynamic behavior of the dense m-ary trees under insertion shows that the average storage utilization tends to 1; that is, the trees become as dense as possible. This motivates the use of the term "dense."

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Section: Basic Definitions and Static Structure Of Dense Multiway Treesmentioning

confidence: 98%

Dense multiway trees

Čulík

Ottmann

Wood

1981

ACM Trans. Database Syst.

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On the number of keys in minimal 2-3 brother trees

Sastry

Murthy

1986

International Journal of Computer Mathematics

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A compendium of key search references

Aoe¹

1990

SIGIR Forum

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How to store and to search, or retrieve, information efficiently is an important problem in computer science because searching is the most time-consuming part of many programs, and the substitution of a good search method for a bad one often leads to a substantial increase in speed. Particularly, a key search technique of finding which record has a special field as its key has been widely used in database management, compiler construction, natural language processing, and many other applications. The aim of this article is to provide a great deal of references, classified by consideration of their problems.

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On a relationship between 2-3 brother trees and dense ternary trees

Cited by 3 publications

References 1 publication

Dense multiway trees

Dense multiway trees

On the number of keys in minimal 2-3 brother trees

A compendium of key search references

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