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 occurs in many important parallel computing/networking applications. In this paper, we look into the issue of realizing all-to-all personalized exchange in optical multistage networks. Advances in electro-optic 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 an optimal scheme for realizing all-to-all personalized exchange in a class of unique-path, selfrouting optical multistage networks crosstalk-free. The basic idea of realizing all-to-all personalized exchange in such a multistage network is to transform it to multiple semi-permutations, each of which can be realized crosstalk-free in a single pass, and take advantage of pipelined message transmission in consecutive passes. As can be seen, the time complexity of our all-to-all personalized exchange algorithms matches the lower bound of the communication delay in this type of network.