OTIS-MOT: an efficient interconnection network for parallel processing

Abstract

Mesh of trees (MOT) is well known for its small diameter, high bisection width, simple decomposability and area universality. On the other hand, OTIS (Optical Transpose Interconnection System) provides an efficient optoelectronic model for massively parallel processing system. In this paper, we present OTIS-MOT as a competent candidate for a two-tier architecture that can take the advantages of both the OTIS and the MOT. We show that an $n^{4}_{-}$ processor OTIS-MOT has diameter 8log?n ?+1 (The base of the logarithm is assumed to be 2 throughout this paper.) and fault diameter 8log?n+2 under single node failure. We establish other topological properties such as bisection width, multiple paths and the modularity. We show that many communication as well as application algorithms can run on this network in comparable time or even faster than other similar tree-based two-tier architectures. The communication algorithms including row/column-group broadcast and one-to-all broadcast are shown to require O(log?n) time, multicast in O(n 2log?n) time and the bit-reverse permutation in O(n) time. Many parallel algorithms for various problems such as finding polynomial zeros, sales forecasting, matrix-vector multiplication and the DFT computation are proposed to map in O(log?n) time. Sorting and prefix computation are also shown to run in O(log?n) time.