Al L

Lower bounds for distributed algorithms for complete networks of processors (i.e., networks where each pair of processors is connected by a communication line) are discussed. We first show an f2(n log n) lower bound for the number of messages required by any algorithm in a given class of distributed algorithms for such networks. This class includes algorithms for problems like finding a leader or constructing a spanning tree. We then show an fIl(n’) lower bound for other problems, like constructing a maximal matching or a Hamiltonian circuit. In proving the lower bounds we are counting the edges which carry messages during the executions of the algorithms (ignoring the actual number of messages carried by each edge). Interestingly, this number is shown to be of the same order of magnitude as the total number of messages needed by these algorithms. The proofs of the lower bounds apply for synchronous networks and for arbitrarily long messages.