Lower bounds for number-in-hand multiparty communication complexity, made easy

In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in the message-passing model, where messages are sent player-to-player. We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as the icost method [5]. For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of Ω(nk) in the blackboard model. For the same problem with AND instead of XOR, we prove a lower bounds of roughly Ω(nk) in the message-passing model (assuming k ≤ n/3200) and Ω(n log k) in the blackboard model. We also prove lower bounds for bit-wise majority, for a graph-connectivity problem, and for other probl...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Jeff M. Phillips, Elad Verbin, Qin Zhang
• Keywords: Algorithms, Communication Protocols, Graph Connectivity, Multiparty Communication Complexity, SODA 2012