Basic operations on a partitioned optical passive stars network with large group size

In a Partitioned Optical Passive Stars (POPS) network, n = dg processors are divided into g groups of d processors each and such a POPS network is denoted by POPS(d, g). There is an optical passive star (OPS) coupler between every pair of groups. Each OPS coupler can receive an optical signal from any one of its source nodes and broadcast the signal to all the destination nodes. The time needed to perform this receive and broadcast is referred to as a time slot and the complexity of an algorithm using the POPS network is measured in terms of number of slots it uses. Since a POPS(d, g) requires g(2) couplers, it is unlikely that in a practical system the number of couplers will be more than the number of processors. In other words, in most practical systems, the group size d will be greater than the number of groups g, i.e., d > rootn > g. Hence, it is important to design fast algorithms for basic operations on such POPS networks with large group sizes. We present several fast algorithms for basic arithmetic operations on POPS(d, g)s such that d > rootn > g. Our algorithms require significantly less number of slots for these operations compared to the best known algorithms for these problems designed by Sahni [8].