Optimal all-to-all personalized exchange in a class of optical multistage networks

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, crosstalk 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 semipermutations 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 O(n) time complexity for n 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.