Self-Simulation for the Passive Optical Star Model

Pascal Berthomé, Th. Duboux, Torben Hagerup, Ilan Newman, Assaf Schuster

Abstract: In the context of parallel computing, optical technology offers simple interconnection schemes with straightforward layouts that support complex logical interconnection patterns. The Passive Optical Star (Pos) is often suggested as a platform for implementing the optical network: logically it offers an all-to-all broadcast capability. We investigate the self-simulation or scalability properties of the Pos. A family of parallel machines is said to be self-simulating or scalable if reducing the number of processors by a factor of k (by going to a smaller member of the family) increases the computation time by a factor of (the optimal) O(k). We present a randomized algorithm for an n-processor Pos that simulates a kn-processor Pos with a slowdown of O(k+log* n) using local control only, thus coming close to the self-simulation ideal of O(k). We also analyze direct algorithms that send messages directly from their origin to their destination; for this case we prove that Θ(k 2) is the exact complexity.