Routing Permutations in Partitioned Optical Passive Star Networks

It is shown that a partitioned optical passive stars (POPS) network with g groups and d processors per group can route any permutation among the n=dg processors in one slot when d=1 and 2[d/g] slots when d>1. The number of slots used is optimal in the worst case, and is at most the double of the optimum for all permutations π such that π(i)≠i, for all i.