Realizing common communication patterns in partitioned optical passive stars (POPS) networks

We consider the problem of realizing several common communication structures in the all-optical Partitioned Optical Passive Stars (POPS) topology. We show that, often, the obvious or "natural" method of implementing a communication pattern in the POPS does not efficiently utilize its communication capabilities. We present techniques which distribute the communication load uniformly in the POPS for four of the most common communication patterns (all-to-all personalized, global reduction operations, ring, and torus). We prove that these techniques provide optimal performance in the sense that they minimize the time required to deliver the messages from each node to its neighbors.