Multiparty Equality Function Computation in Networks with Point-to-Point Links

TL;DR

This paper investigates the communication complexity of the multiparty equality function in a realistic network model with point-to-point links, introducing new techniques to analyze protocol efficiency in such settings.

Contribution

It presents novel analytical techniques for multiparty equality function computation in point-to-point networks, extending beyond traditional two-party methods.

Findings

Traditional two-party techniques are insufficient for this model.

New techniques significantly reduce the protocol space for analysis.

Some instances of the MEQ problem are effectively studied with these methods.

Abstract

In this report, we study the multiparty communication complexity problem of the multiparty equality function (MEQ): EQ(x_1,...,x_n) = 1 if x_1=...=x_n, and 0 otherwise. The input vector (x_1,...,x_n) is distributed among n>=2 nodes, with x_i known to node i, where x_i is chosen from the set {1,...,M}, for some integer M>0. Instead of the "number on the forehand" model, we consider a point-to-point communication model (similar to the message passing model), which we believe is more realistic in networking settings. We assume a synchronous fully connected network of n nodes, the node IDs (identifiers) are common knowledge. We assume that all point-to-point communication channels/links are private such that when a node transmits, only the designated recipient can receive the message. The identity of the sender is known to the recipient. We demonstrate that traditional techniques generalized from two-party communication complexity problem are not sufficient to obtain tight bounds under the point-to-point communication model. We then introduce techniques which significantly reduce the space of protocols to study. These techniques are used to study some instances of the MEQ problem.