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A Bijection for the Evolution of B-Trees

Authors Fabian Burghart , Stephan Wagner

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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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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.

Cite As Get BibTex

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

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

Funding

  • Burghart, Fabian: F. Burghart has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034253.
  • Wagner, Stephan: Supported by the Swedish research council (VR), grant 2022-04030.

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