Crossing the logarithmic barrier for dynamic boolean data structure lower bounds

Kasper Green Larsen, Omri Weinstein, Huacheng Yu

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

13 Scopus citations

Abstract

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new approach and use it to prove a Ω (lg1.5 n) lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting over F2 (Pǎtraşcu, 2007). Proving an (lg n) lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai Pǎtraşcu’s obituary (Thorup, 2013). This result also implies the first (lg n) lower bound for the classical 2D range counting problem, one of the most fundamental data structure problems in computational geometry and spatial databases. We derive similar lower bounds for boolean versions of dynamic polynomial evaluation and 2D rectangle stabbing, and for the (non-boolean) problems of range selection and range median. Our technical centerpiece is a new way of “weakly" simulating dynamic data structures using efficient one-way communication protocols with small advantage over random guessing. This simulation involves a surprising excursion to low-degree (Chebyshev) polynomials which May be of independent interest, and offers an entirely new algorithmic angle on the “cell sampling" method of Panigrahy et al. (2010).

Original languageAmerican English
Title of host publicationSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
EditorsMonika Henzinger, David Kempe, Ilias Diakonikolas
PublisherAssociation for Computing Machinery
Pages485-492
Number of pages8
ISBN (Electronic)9781450355599
DOIs
StatePublished - 20 Jun 2018
Externally publishedYes
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: 25 Jun 201829 Jun 2018

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference50th Annual ACM Symposium on Theory of Computing, STOC 2018
Country/TerritoryUnited States
CityLos Angeles
Period25/06/1829/06/18

Bibliographical note

Publisher Copyright:
© 2018 Association for Computing Machinery.

Keywords

  • Cell probe complexity
  • Data structures
  • Dynamic problems
  • Lower bounds
  • Range searching

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