All-to-all personalized communication on multistage interconnection networks

Abstract

In parallel/distributed computing systems, the all-to-all personalized communication (or complete exchange) is required in numerous applications of parallel processing. In this paper, we consider this problem for log N stage Multistage Interconnection Networks (MINs). It is proved that the set of admissible permutations for a MIN can be partitioned in Latin Squares. Since routing permutations belonging to a Latin Square provides the all-to-all personalized communication, a method to realize the complete exchange with time complexity O( N), that is optimal, can be derived. This method, compared with other ones in literature, does not necessitate of neither pre-computation nor memory allocation to record the Latin Square, because an explicit construction of it is not required; furthermore it is applicable to any log N stage multistage networks since it is independent of the topology.