Dynamic Binary Search Trees: Improved Lower Bounds for the Greedy-Future Algorithm

Yaniv Sadeh*, Haim Kaplan*

*Corresponding author for this work

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

Abstract

Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be dynamic (i.e. change by rotations between searches), we still do not know how to compute the optimal algorithm (OPT) for a given sequence. One of the candidate algorithms whose serving cost is suspected to be optimal up-to a (multiplicative) constant factor is known by the name Greedy Future (GF). In an equivalent geometric way of representing queries on BSTs, GF is in fact equivalent to another algorithm called Geometric Greedy (GG). Most of the results on GF are obtained using the geometric model and the study of GG. Despite this intensive recent fruitful research, the best lower bound we have on the competitive ratio of GF is 43. Furthermore, it has been conjectured that the additive gap between the cost of GF and OPT is only linear in the number of queries. In this paper we prove a lower bound of 2 on the competitive ratio of GF, and we prove that the additive gap between the cost of GF and OPT can be Ω(m · log log n) where n is the number of items in the tree and m is the number of queries.

Original languageEnglish
Title of host publication40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023
EditorsPetra Berenbrink, Patricia Bouyer, Anuj Dawar, Mamadou Moustapha Kante
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772662
DOIs
StatePublished - 1 Mar 2023
Event40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023 - Hamburg, Germany
Duration: 7 Mar 20239 Mar 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume254
ISSN (Print)1868-8969

Conference

Conference40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023
Country/TerritoryGermany
CityHamburg
Period7/03/239/03/23

Keywords

  • Binary Search Trees
  • Dynamic Optimality Conjecture
  • Geometric Greedy
  • Greedy Future
  • Lower Bounds

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