Parallel algorithms with irregular interconnections and optical technology

Abstract

We consider the implementation of fast parallel algorithms. We make the case that irregular interconnections result in faster parallel algorithms; consequently, optical technologies that can support such randomlike interconnections are preferable. We demonstrate this by selecting a problem which has very fast parallel algorithms when irregular interconnections are used, and by suggesting certain optical technologies that can support such irregular interconnections for implementing these fast parallel algorithms. (On the other hand, it is well known that any technology that can only support regular and planar interconnections cannot achieve the same speedup.) The problem is that of approximately halving a sequence of numbers. This problem comes up as a natural subproblem in the optimal sorting algorithm of Ajtai, Komlos, and Szemeredi.1 We use probabilistic means to construct the interconnections necessary for the approximate halver problem and certify their properties by computing their spectrum. We also show that the interconnection pattern underlies several other fast parallel algorithms such as sorting, selection, load balancing, distributed consensus, and error-correcting codes. We then suggest that POEM (programmable optoelectronic multiprocessor) technology is capable of implementing such randomlike interconnections.