Mapping hypercube computations onto Partitioned Optical Passive Star Networks

This paper shows that an n=2^k processor Partitioned Optical Passive Stars (POPS) network with g groups and d processors per group can simulate either a mono-directional move of an n processor hypercube or a bi-directional move of an n/2 processor hypercube using one slot when d=1 and ⌈d/g ⌉ slots when d>1. Moreover, as a direct application of the simulation, it is shown how a POPS(d, g) network, n=dg and d ≤ q, can compute the prefix sums of n data values in log_2 n + O(1) slots, faster than the best previously known ad-hoc algorithm for this problem.