Polynomial data structure lower bounds in the group model

Alexander Golovnev, Gleb Posobin, Oded Regev, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Proving super-logarithmic data structure lower bounds in the static group model has been a fundamental challenge in computational geometry since the early 80's. We prove a polynomial (n{Omega(1)}) lower bound for an explicit range counting problem of n{3} convex polygons in mathbb{R}{2} (each with n{tilde{O}(1)} facets/semialgebraic-complexity), against linear storage arithmetic data structures in the group model. Our construction and analysis are based on a combination of techniques in Diophantine approximation, pseudorandomness, and compressed sensing-in particular, on the existence and partial derandomization of optimal binary compressed sensing matrices in the polynomial sparsity regime (k=n{1-delta}). As a byproduct, this establishes a (logarithmic) separation between compressed sensing matrices and the stronger RIP property.

Original languageEnglish (US)
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
PublisherIEEE Computer Society
Pages740-751
Number of pages12
ISBN (Electronic)9781728196213
DOIs
StatePublished - Nov 2020
Event61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States
Duration: Nov 16 2020Nov 19 2020

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2020-November
ISSN (Print)0272-5428

Conference

Conference61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
Country/TerritoryUnited States
CityVirtual, Durham
Period11/16/2011/19/20

Keywords

  • compressed sensing
  • computational geometry
  • data structures
  • pseudorandomness

ASJC Scopus subject areas

  • Computer Science(all)

Fingerprint

Dive into the research topics of 'Polynomial data structure lower bounds in the group model'. Together they form a unique fingerprint.

Cite this