Routing permutations with link-disjoint and node-disjoint paths in a class of self-routable networks

Abstract

High-speed interconnects have been gaining much attention from the computer industry recently as interconnects are becoming a limiting factor to the performance of modern computer systems. This trend will even continue in the near future as technology improves. In this paper, we consider efficiently routing permutations in a class of switch-based interconnects. Permutation is an important communication pattern in parallel and distributed computing systems. We present a generic approach to realizing arbitrary permutations in a class of unique-path, self-routable multistage networks. We consider routing arbitrary permutations with link-disjoint paths and node-disjoint paths in such interconnects in a minimum number of passes. In particular, routing with node-disjoint paths has important applications in the emerging optical interconnects. We employ and further expand the Latin square technique used in the all-to-all personalized exchange algorithms for this class of multistage networks for general permutation routing. The implementation is optimal in number of passes and near-optimal in network transmission time.