An improved protocol for the exactly-N problem

Nati Linial; Adi Shraibman

doi:10.4230/LIPIcs.CCC.2021.2

An improved protocol for the exactly-N problem

Nati Linial^*, Adi Shraibman^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

2 Scopus citations

Abstract

In the 3-players exactly-N problem the players need to decide whether x + y + z = N for inputs x, y, z and fixed N. This is the first problem considered in the multiplayer Number On the Forehead (NOF) model. Even though this is such a basic problem, no progress has been made on it throughout the years. Only recently have explicit protocols been found for the first time, yet no improvement in complexity has been achieved to date. The present paper offers the first improved protocol for the exactly-N problem. This improved protocol has also interesting consequences in additive combinatorics. As we explain below, it yields a higher lower bound on the possible density of corner-free sets in [N] × [N].

Original language	English
Title of host publication	36th Computational Complexity Conference, CCC 2021
Editors	Valentine Kabanets
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	2:1-2:8
Number of pages	8
ISBN (Electronic)	9783959771931
DOIs	https://doi.org/10.4230/LIPIcs.CCC.2021.2
State	Published - 1 Jul 2021
Event	36th Computational Complexity Conference, CCC 2021 - Virtual, Toronto, Canada Duration: 20 Jul 2021 → 23 Jul 2021

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	200
ISSN (Print)	1868-8969

Conference

Conference	36th Computational Complexity Conference, CCC 2021
Country/Territory	Canada
City	Virtual, Toronto
Period	20/07/21 → 23/07/21

Bibliographical note

Publisher Copyright:
© Nati Linial and Adi Shraibman; licensed under Creative Commons License CC-BY 4.0

Keywords

Communication complexity
Corner-free sets
Number-on-the-forehead

Access to Document

10.4230/LIPIcs.CCC.2021.2

Cite this

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title = "An improved protocol for the exactly-N problem",

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Linial, N & Shraibman, A 2021, An improved protocol for the exactly-N problem. in V Kabanets (ed.), 36th Computational Complexity Conference, CCC 2021., 2, Leibniz International Proceedings in Informatics, LIPIcs, vol. 200, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 2:1-2:8, 36th Computational Complexity Conference, CCC 2021, Virtual, Toronto, Canada, 20/07/21. https://doi.org/10.4230/LIPIcs.CCC.2021.2

An improved protocol for the exactly-N problem. / Linial, Nati; Shraibman, Adi.
36th Computational Complexity Conference, CCC 2021. ed. / Valentine Kabanets. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2021. p. 2:1-2:8 2 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 200).

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

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An improved protocol for the exactly-N problem

Abstract

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Bibliographical note

Keywords

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