TY - GEN

T1 - The communication complexity of multiparty set disjointness under product distributions

AU - Dershowitz, Nachum

AU - Oshman, Rotem

AU - Roth, Tal

N1 - Publisher Copyright:
© 2021 ACM.

PY - 2021/6/15

Y1 - 2021/6/15

N2 - In the multiparty number-in-hand set disjointness problem, we have k players, with private inputs X1,...,Xk ? [n]. The players' goal is to check whether ?=1k X? = .... It is known that in the shared blackboard model of communication, set disjointness requires ?(n logk + k) bits of communication, and in the coordinator model, it requires ?(kn) bits. However, these two lower bounds require that the players' inputs can be highly correlated. We study the communication complexity of multiparty set disjointness under product distributions, and ask whether the problem becomes significantly easier, as it is known to become in the two-party case. Our main result is a nearly-tight bound of (n1-1/k + k) for both the shared blackboard model and the coordinator model. This shows that in the shared blackboard model, as the number of players grows, having independent inputs helps less and less; but in the coordinator model, when k is very large, having independent inputs makes the problem much easier. Both our upper and our lower bounds use new ideas, as the original techniques developed for the two-party case do not scale to more than two players.

AB - In the multiparty number-in-hand set disjointness problem, we have k players, with private inputs X1,...,Xk ? [n]. The players' goal is to check whether ?=1k X? = .... It is known that in the shared blackboard model of communication, set disjointness requires ?(n logk + k) bits of communication, and in the coordinator model, it requires ?(kn) bits. However, these two lower bounds require that the players' inputs can be highly correlated. We study the communication complexity of multiparty set disjointness under product distributions, and ask whether the problem becomes significantly easier, as it is known to become in the two-party case. Our main result is a nearly-tight bound of (n1-1/k + k) for both the shared blackboard model and the coordinator model. This shows that in the shared blackboard model, as the number of players grows, having independent inputs helps less and less; but in the coordinator model, when k is very large, having independent inputs makes the problem much easier. Both our upper and our lower bounds use new ideas, as the original techniques developed for the two-party case do not scale to more than two players.

KW - communication complexity

KW - product distributions

KW - set disjointness

UR - http://www.scopus.com/inward/record.url?scp=85108162860&partnerID=8YFLogxK

U2 - 10.1145/3406325.3451106

DO - 10.1145/3406325.3451106

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85108162860

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1194

EP - 1207

BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Khuller, Samir

A2 - Williams, Virginia Vassilevska

PB - Association for Computing Machinery

T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -