The universality of a class of (2log/sub 2/N-1)-stage interconnection networks

Abstract

The performance of a highly-parallel multiprocessor system depends heavily on the efficiency of its interconnection network. We focus on an N/spl times/N, (2log/sub 2/N-1)-stage interconnection network. A concatenated (2log/sub 2/N-1)-stage interconnection network (denoted by (/spl Delta//spl oplus//spl Delta/')) is a combination of two, cube-type networks with the rightmost stage of /spl Delta/ and the left most stage of /spl Delta/' overlapped. Despite the better performance, (2log/sub 2/N-1)-stage networks have not been studied enough to explore all the important topological properties. We study the topological structure of (/spl Delta//spl oplus//spl Delta/') and then state, formulate and prove a very important property, the interstage correlation. Interstage correlation is the relationship between output line bits of the left network SEs and input line bits of the right network SEs in (/spl Delta//spl oplus//spl Delta/'). Interstage correlation can be used as the criteria of classification for (2log/sub 2/N-1)-stage networks. Until now, research in this field was focused only on the class of Benes-equivalent networks. This class is just a small subset of a set of all possible interconnection networks. We formulate interstage correlation such that it can be used to classify many possible (2log/sub 2/N-1)-stage networks and discuss their topological equivalence.