Explicit exponential lower bounds for exact hyperplane covers

Benjamin E. Diamond; Amir Yehudayoff

doi: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

Access to Document

10.1016/j.disc.2022.113114

Cite this

@article{4333b2fbd2b444f09504dd39e294fa2f,

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",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = nov,

doi = "10.1016/j.disc.2022.113114",

language = "الإنجليزيّة",

volume = "345",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "11",

}

TY - JOUR

T1 - Explicit exponential lower bounds for exact hyperplane covers

AU - Diamond, Benjamin E.

AU - Yehudayoff, Amir

PY - 2022/11

Y1 - 2022/11

N2 - 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.

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

KW - Exact hyperplane covers

KW - Lower bounds

UR - http://www.scopus.com/inward/record.url?scp=85135897436&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2022.113114

DO - 10.1016/j.disc.2022.113114

M3 - مقالة

SN - 0012-365X

VL - 345

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

Access to Document

Other files and links

Fingerprint

Cite this