Explicit exponential lower bounds for exact hyperplane covers

Benjamin E. Diamond; Amir Yehudayoff

doi:https://doi.org/10.1016/j.disc.2022.113114

Explicit exponential lower bounds for exact hyperplane covers

Research output: Contribution to journal › Article › peer-review

Abstract

We describe an explicit and simple subset of the discrete hypercube which cannot be exactly covered by fewer than exponentially many hyperplanes. The proof exploits a connection to communication complexity, and relies heavily on Razborov's lower bound for disjointness.

Original language	English
Article number	113114
Journal	Discrete Mathematics
Volume	345
Issue number	11
DOIs	https://doi.org/10.1016/j.disc.2022.113114
State	Published - Nov 2022
Externally published	Yes

Keywords

Communication complexity
Exact hyperplane covers
Lower bounds

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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https://doi.org/10.1016/j.disc.2022.113114

Cite this

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title = "Explicit exponential lower bounds for exact hyperplane covers",

abstract = "We describe an explicit and simple subset of the discrete hypercube which cannot be exactly covered by fewer than exponentially many hyperplanes. The proof exploits a connection to communication complexity, and relies heavily on Razborov's lower bound for disjointness.",

keywords = "Communication complexity, Exact hyperplane covers, Lower bounds",

author = "Diamond, {Benjamin E.} and Amir Yehudayoff",

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year = "2022",

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AB - We describe an explicit and simple subset of the discrete hypercube which cannot be exactly covered by fewer than exponentially many hyperplanes. The proof exploits a connection to communication complexity, and relies heavily on Razborov's lower bound for disjointness.

KW - Communication complexity

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KW - Lower bounds

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DO - https://doi.org/10.1016/j.disc.2022.113114

M3 - مقالة

SN - 0012-365X

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 11

M1 - 113114

ER -

Explicit exponential lower bounds for exact hyperplane covers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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