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<p><b>Abstract</b>—In a <it>Partitioned Optical Passive Stars (POPS)</it> network, <tmath>n=dg</tmath> processors are divided into <tmath>g</tmath> groups of <tmath>d</tmath> processors each, and such a POPS network is denoted by <tmath>POPS(d,g)</tmath>. There is an optical passive star (OPS) coupler between every pair of groups. Hence, a <tmath>POPS(d,g)</tmath> requires <tmath>g^{2}</tmath> couplers. It is likely that, in a practical system, the number of couplers will be less than the number of processors, i.e., <tmath>d>\sqrt n>g</tmath> 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 <it>data sum</it>, <it>prefix sum</it>, and <it>permutation routing</it> on a <tmath>POPS(d,g)</tmath> such that <tmath>d>\sqrt n>g</tmath>. Our data sum and prefix sum algorithms improve upon the best known algorithms for these problems. 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.</p>
Optical computing, partitioned optical passive stars network, data sum, prefix sum, permutation routing.

S. Soundaralakshmi and A. Datta, "Summation and Routing on a Partitioned Optical Passive Stars Network with Large Group Size," in IEEE Transactions on Parallel & Distributed Systems, vol. 14, no. , pp. 1275-1285, 2003.
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