Settling the relationship between wilber’s bounds for dynamic optimality

Victor Lecomte, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

In FOCS 1986, Wilber proposed two combinatorial lower bounds on the operational cost of any binary search tree (BST) for a given access sequence X ∈ [n]m. Both bounds play a central role in the ongoing pursuit of the dynamic optimality conjecture (Sleator and Tarjan, 1985), but their relationship remained unknown for more than three decades. We show that Wilber’s Funnel bound dominates his Alternation bound for all X, and give a tight Θ(lg lg n) separation for some X, answering Wilber’s conjecture and an open problem of Iacono, Demaine et. al. The main ingredient of the proof is a new symmetric characterization of Wilber’s Funnel bound, which proves that it is invariant under rotations of X. We use this characterization to provide initial indication that the Funnel bound matches the Independent Rectangle bound (Demaine et al., 2009), by proving that when the Funnel bound is constant, IRB is linear. To the best of our knowledge, our results provide the first progress on Wilber’s conjecture that the Funnel bound is dynamically optimal (1986).

Original languageAmerican English
Title of host publication28th Annual European Symposium on Algorithms, ESA 2020
EditorsFabrizio Grandoni, Grzegorz Herman, Peter Sanders
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771627
DOIs
StatePublished - 1 Aug 2020
Externally publishedYes
Event28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, Italy
Duration: 7 Sep 20209 Sep 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume173
ISSN (Print)1868-8969

Conference

Conference28th Annual European Symposium on Algorithms, ESA 2020
Country/TerritoryItaly
CityVirtual, Pisa
Period7/09/209/09/20

Bibliographical note

Publisher Copyright:
© Victor Lecomte and Omri Weinstein.

Keywords

  • Binary search trees
  • Dynamic optimality
  • Lower bounds
  • data structures

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