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

3 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 method for proving dynamic cell probe lower bounds and use it to prove a Ω(lg1.5n) 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 ([Pat07]). Proving an ω(lg n) lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai Pǎtraşcu's obituary [Tho13]. This result also implies the first ω(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 (Chebychev) polynomials which may be of independent interest, and offers an entirely new algorithmic angle on the 'cell sampling' method of Panigrahy et al. [PTW10].

Original languageAmerican English
Title of host publication2018 Information Theory and Applications Workshop, ITA 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728101248
DOIs
StatePublished - 23 Oct 2018
Externally publishedYes
Event2018 Information Theory and Applications Workshop, ITA 2018 - San Diego, United States
Duration: 11 Feb 201816 Feb 2018

Publication series

Name2018 Information Theory and Applications Workshop, ITA 2018

Conference

Conference2018 Information Theory and Applications Workshop, ITA 2018
Country/TerritoryUnited States
CitySan Diego
Period11/02/1816/02/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

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