Repackable Log2(N, m, p) Networks and Wide-Sense Nonblocking Log2(8, 0, p) Networks

Abstract

The repackable Log2(N, 0, p) network, wherein repacking activities are required during departures but not upon arrivals, was proposed by Lin and Lea in a study on multi-Log2N networks. Due to their complexity, Log2(N, m, p) networks are considerably more difficult to analyze compared with Log2(N, 0, p) networks. In this paper, we successfully extend the repackable Log2(N, 0, p) networks to Log2(N, m, p) networks. In addition, the proposed routing algorithm is shown to be an optimal algorithm according to the total number of planes required. Furthermore, an analysis tool is proposed for studying repackable Log2(N, m, p) networks and is applied to show that each wide-sense nonblocking Log2(8, 0, p) network requires the same total number of planes as a strictly nonblocking network under any possible routing strategy.