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Patricia’s Bad Distributions

Authors Louigi Addario-Berry , Pat Morin , Ralph Neininger

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Author Details

Louigi Addario-Berry
  • Department of Mathematics and Statistics, McGill University, Montréal, Canada
Pat Morin
  • School of Computer Science, Carleton University, Ottawa, Canada
Ralph Neininger
  • Institute of Mathematics, Goethe University Frankfurt, Germany

Acknowledgements

This research was mainly done during the Sixteenth Annual Workshop on Probability and Combinatorics at McGill University’s Bellairs Institute in Holetown, Barbados. We thank Bellairs Institute for its hospitality and support. We also thank the referees and Jasmin Straub for comments on a draft of this note.

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Louigi Addario-Berry, Pat Morin, and Ralph Neininger. Patricia’s Bad Distributions. 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. 25:1-25:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.25

Abstract

The height of a random PATRICIA tree built from independent, identically distributed infinite binary strings with arbitrary diffuse probability distribution μ on {0,1}^ℕ is studied. We show that the expected height grows asymptotically sublinearly in the number of leaves for any such μ, but can be made to exceed any specific sublinear growth rate by choosing μ appropriately.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
Keywords
  • PATRICIA tree
  • random tree
  • height of tree
  • analysis of algorithms

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