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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. Hence, a POPS(d,g) requires g2 couplers. It is likely that, in a practical system, the number of couplers will be less than the number of processors, i.e., d>√n>g and the number of groups will be smaller than the number of processors in a group. Hence, it is important to design fast algorithms for basic operations on such POPS networks with large group size. We present fast algorithms for data sum, prefix sum, and permutation routing on a POPS(d,g) such that d>√n>g. Our data sum and prefix sum algorithms improve upon the best known algorithms for these problems designed by Sahni (2000). Permutation routing can be solved on a POPS network by simulating a hypercube sorting algorithm. Our algorithm for permutation routing is more efficient compared to this simulated hypercube sorting algorithm.