Tribes is hard in the message passing model

Sagnik Mukhopadhyay

Abstract

We consider the point-to-point message passing model of communication in which there are k processors with individual private inputs, each n-bit long. Each processor is located at the node of an underlying undirected graph and has access to private random coins. An edge of the graph is a private channel of communication between its endpoints. The processors have to compute a given function of all their inputs by communicating along these channels. While this model has been widely used in distributed computing, strong lower bounds on the amount of communication needed to compute simple functions have just begun to appear.

In this talk, we will see a tight lower bound of Theta(kn) on the communication needed for computing the Tribes function, when the underlying graph is a star of k + 1 nodes that has k leaves with inputs and a center with no input. Lower bound on this topology easily implies comparable bounds for