Polynomial data structure lower bounds in the group model

Alexander Golovnev; Gleb Posobin; Oded Regev; Omri Weinstein

doi:10.1109/FOCS46700.2020.00074

Polynomial data structure lower bounds in the group model

Alexander Golovnev, Gleb Posobin, Oded Regev, Omri Weinstein

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
Publisher	IEEE Computer Society
Pages	740-751
Number of pages	12
ISBN (Electronic)	9781728196213
DOIs	https://doi.org/10.1109/FOCS46700.2020.00074
State	Published - Nov 2020
Externally published	Yes
Event	61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States Duration: 16 Nov 2020 → 19 Nov 2020

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	2020-November
ISSN (Print)	0272-5428

Conference

Conference	61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
Country/Territory	United States
City	Virtual, Durham
Period	16/11/20 → 19/11/20

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

Keywords

compressed sensing
computational geometry
data structures
pseudorandomness

Access to Document

10.1109/FOCS46700.2020.00074

Cite this

Golovnev, A., Posobin, G., Regev, O., & Weinstein, O. (2020). Polynomial data structure lower bounds in the group model. In Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020 (pp. 740-751). Article 9317940 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2020-November). IEEE Computer Society. https://doi.org/10.1109/FOCS46700.2020.00074

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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.",

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Golovnev, A, Posobin, G, Regev, O & Weinstein, O 2020, Polynomial data structure lower bounds in the group model. in Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020., 9317940, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2020-November, IEEE Computer Society, pp. 740-751, 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Virtual, Durham, United States, 16/11/20. https://doi.org/10.1109/FOCS46700.2020.00074

Polynomial data structure lower bounds in the group model. / Golovnev, Alexander; Posobin, Gleb; Regev, Oded et al.
Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020. IEEE Computer Society, 2020. p. 740-751 9317940 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2020-November).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Polynomial data structure lower bounds in the group model

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