A Tight Bound for Set Disjointness in the Message-Passing Model

In a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed computing and in secure multiparty computation, lower bounds on communication complexity in this model and related models have been somewhat scarce. In recent work [25], [29], [30], strong lower bounds of the form Ω(n·k) were obtained for several functions in the message-passing model; however, a lower bound on the classical set disjointness problem remained elusive. In this paper, we prove a tight lower bound of Ω(n · k) for the set disjointness problem in the message passing model. Our bound is obtained by developing information complexity tools for the message-passing model and proving an information complexity lower bound for set disjointness.