eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-07-18
10:1
10:15
10.4230/LIPIcs.AofA.2024.10
article
A Bijection for the Evolution of B-Trees
Burghart, Fabian
1
https://orcid.org/0000-0003-1977-2345
Wagner, Stephan
2
3
https://orcid.org/0000-0001-5533-2764
Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands
Institute of Discrete Mathematics, TU Graz, Austria
Department of Mathematics, Uppsala University, Sweden
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol302-aofa2024/LIPIcs.AofA.2024.10/LIPIcs.AofA.2024.10.pdf
B-trees
histories
increasing trees
bijection
asymptotic enumeration
tree statistics