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<p><b>Abstract</b>—All-to-all personalized exchange is one of the most dense collective communication patterns and it occurs in many important parallel computing/networking applications. In this paper, we look into the issue of realizing an all-to-all personalized exchange in a class of optical multistage networks. Advances in electrooptic technologies have made optical communication a promising networking choice to meet the increasing demands for high channel bandwidth and low communication latency of high-performance computing/communication applications. Although optical multistage networks hold great promise and have demonstrated advantages over their electronic counterpart, they also hold their own challenges. Due to the unique properties of optics, <it>crosstalk</it> in optical switches should be avoided to make them work properly. In this paper, we will provide a systematic scheme for realizing an all-to-all personalized exchange in a class of unique-path optical multistage networks crosstalk-free. The basic idea of realizing an all-to-all personalized exchange in such a multistage network is to transform it to multiple <it>semipermutations</it> and ensure that each of them can be realized crosstalk-free in a single pass. As can be seen, the all-to-all personalized exchange algorithm we propose has <tmath>$O(n)$</tmath> time complexity for <tmath>$n$</tmath> processors, which is optimal for an all-to-all personalized exchange. The optimal time complexity combined with the property of a single input/output port per processor suggests that a multistage network could be a better choice for implementing an all-to-all personalized exchange due to its shorter communication latency and better scalability.</p>
Optical networks, multistage networks, all-to-all communication, all-to-all personalized exchange, permutation, semipermutation, Latin square, crosstalk.

Y. Yang and J. Wang, "Optimal All-to-All Personalized Exchange in a Class of Optical Multistage Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 567-582, 2001.
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