Efficient optical communication in parallel computers

We study the problem of interprocessor communication in a parallel computer model suggested by recent advances in optical technology. The units of the computer (processors with local memory) communicate with each other by transmitting messages. A processor can transmit a message to any other processor, and transmission takes constant time. If two or more processors try to send a message to the same processor no transmission is successful and retransmission must occur. We show how to implement an extremely simple and efficient form of randomized routing in this model. We study, in particular, the problem of realizing arbitrary h-relations. In an h-relation, each processor is the source as well as the destination of at most h messages. We propose a simple and practical distributed randomized algorithm for realizing arbitrary h-relations on an n-processor such network within O(h + log n log log n) parallel communication steps. Our algorithm is pure in the sense that no information aside from actual messages is transmitted between processors. Anderson and Miller [1] and Valiant [19] have derived a @(h + log n) algorithm for the same problem, which achieves optimality for a slightly larger range of h. Their algorithm is complicated as opposed to ours that we believe to be practical. Optimal interprocessor communication algorithms in realistic models of parallel computers are not only interesting in their own sake, they are one of the main components in optimally simulating PRAMs as well aa implementing Valiant's bulk-synchronous parallel model [13, 19, 18]. 1 Introduction Optics has been used in the design of special purpose computing devices for quite some time now, especially in the field of signal processing. Recent technological advances make it also an appealing alternative to electronics in the design of general purpose computers. The use of optics has been suggested in such diverse areas as storage, processing, and for providing communica-t put of this ~e~e=ch wss done ~hile the second author WVM Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice k given that copying is by permission of the Association for Computing Machinery. To copy otherwise , or to republish, requires a fee andlor specific permission. tion between different modules within computer systems. The use of optical interconnects …