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

Abstract

The repackable Log 2 (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-Log 2 N networks. Due to their complexity, Log 2 (N, m, p) networks are considerably more difficult to analyze compared with Log 2 (N, 0, p) networks. In this paper, we successfully extend the repackable Log 2 (N, 0, p) networks to Log 2 (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 Log 2 (N, m, p) networks and is applied to show that each wide-sense nonblocking Log 2 (8, 0, p) network requires the same total number of planes as a strictly nonblocking network under any possible routing strategy.