Embedding rings and meshes in partitioned optical passive stars networks

We consider the problem of embedding ring and torus communication structures onto the all-optical Partitioned Optical Passive Stars (POPS) topology. We show that the natural embedding, which maps the nodes in the ring or torus directly onto the POPS, does not result in an optimal embedding, and thus does not efficiently utilize the communication capabilities of the POPS. For the ring structure, we present an alternating-pair embedding technique which distributes the communication load uniformly in the POPS. We then apply a slightly modified version of the alternating-pair technique to the embedding of tori onto POPS networks. We prove that both embeddings are optimal, in the sense that they minimize the time required to deliver the messages from each node to its neighbors.