Lower bounds on communication complexity in distributed computer networks

The main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks. This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array. Applications of this technique yield optimal bounds on the communication complexity of merging, ranking, uniqueness, and triangle-detection problems on a ring of processors. Nontrivial near-optimal lower bounds on the communication complexity of distinctness, merging, and ranking on meshes and complete binary trees are also derived.