Abstract Optimal Broadcast and Summation in the LogP Model

Abstract

In many distributed-memory parallel computers the only built-in communication primitive is point-to-point message transmission, and more powerful operations such asbroa&ast and synchronization must be realized using this primitive. Whhin the LogP model of parallel computation we present algorithms that yield optimal communication schedules for several broadcast and synchronization operations. Most of our algorithms arc the absolutely best possible in that not even the constant factors can be improved upon. For one particular broadcast problem, called continuous broadcast, the optimality of our algorithm is not yet completely proven, although proofs have been achieved for a certain range of pararnetem. We also devise an optimal algorithm for summin g or, more generally, applying a non~ommumtive associative binary operator to a set of operands.