A Bijection for the Evolution of B-Trees

Burghart, Fabian; Wagner, Stephan

doi:10.4230/LIPIcs.AofA.2024.10

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Document Identifiers

DOI: 10.4230/LIPIcs.AofA.2024.10
URN: urn:nbn:de:0030-drops-204451

Author Details

Fabian Burghart

Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands

Stephan Wagner

Institute of Discrete Mathematics, TU Graz, Austria
Department of Mathematics, Uppsala University, Sweden

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Fabian Burghart and Stephan Wagner. A Bijection for the Evolution of B-Trees. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.10

Abstract

A B-tree is a type of search tree where every node (except possibly for the root) contains between m and 2m keys for some positive integer m, and all leaves have the same distance to the root. We study sequences of B-trees that can arise from successively inserting keys, and in particular present a bijection between such sequences (which we call histories) and a special type of increasing trees. We describe the set of permutations for the keys that belong to a given history, and also show how to use this bijection to analyse statistics associated with B-trees.

Subject Classification

ACM Subject Classification

Mathematics of computing → Enumeration
Theory of computation → Randomness, geometry and discrete structures
Theory of computation → Data structures design and analysis

Keywords

B-trees
histories
increasing trees
bijection
asymptotic enumeration
tree statistics

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