LIPIcs.AofA.2024.10.pdf
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A Bijection for the Evolution of B-Trees
Authors
Fabian Burghart 
,
Stephan Wagner
-
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Volume:
35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-07-18
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Author Details
- Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands
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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
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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