eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-08
2:1
2:8
10.4230/LIPIcs.CCC.2021.2
article
An Improved Protocol for the Exactly-N Problem
Linial, Nati
1
Shraibman, Adi
2
Hebrew University of Jerusalem, Israel
The Academic College of Tel-Aviv-Yaffo, Israel
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].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol200-ccc2021/LIPIcs.CCC.2021.2/LIPIcs.CCC.2021.2.pdf
Communication complexity
Number-On-the-Forehead
Corner-free sets