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The Diameter of Caterpillar Associahedra

Author Benjamin Aram Berendsohn

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Author Details

Benjamin Aram Berendsohn
  • Institut für Informatik, Freie Universität Berlin, Germany

Funding

Work supported by DFG grant KO 6140/1-1.

Acknowledgements

I would like to thank László Kozma for helpful discussions and suggestions.

Cite As Get BibTex

Benjamin Aram Berendsohn. The Diameter of Caterpillar Associahedra. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SWAT.2022.14

Abstract

The caterpillar associahedron 𝒜(G) is a polytope arising from the rotation graph of search trees on a caterpillar tree G, generalizing the rotation graph of binary search trees (BSTs) and thus the conventional associahedron. We show that the diameter of 𝒜(G) is Θ(n + m ⋅ (H+1)), where n is the number of vertices, m is the number of leaves, and H is the entropy of the leaf distribution of G.
Our proofs reveal a strong connection between caterpillar associahedra and searching in BSTs. We prove the lower bound using Wilber’s first lower bound for dynamic BSTs, and the upper bound by reducing the problem to searching in static BSTs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
  • Theory of computation → Data structures design and analysis
Keywords
  • Graph Associahedra
  • Binary Search Trees
  • Elimination Trees

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References

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