Communication Complexity: From Two-Party to Multiparty

Abstract

We consider the multiparty communication complexity model, where k players holding inputs x ₁,...,x _k communicate to compute the value f(x ₁,...,x _k ) of a function f known to all of them.

Yao’s classic two-party communication complexity model [3] is the special case k = 2 (see also [2]). In the first part of the talk, we survey some basic results regarding the two-party model, emphasizing methods for proving lower-bounds.

In the second part of the talk, we consider the case where there are at least three parties (k ≥ 3). The main lower bound technique for the communication complexity of such multiparty problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. We discuss the power of partition arguments for both deterministic and randomized protocols. (This part is based on a joint work with Jan Draisma and Enav Weinreb [1].)