EFFICIENT ROUTING ALGORITHMS for GENERALIZED SHUFFLE-EXCHANGE NETWORKS

The shuffle-exchange network has been proposed as a popular architecture for multistage interconnection networks. In 1991, Padmanabhan introduced the generalized shuffle-exchange network (GSEN) and proposed an efficient routing algorithm. Later, Chen et al. further enhanced the GSEN with bidirectional links and proposed the bidirectional GSEN (BGSEN). A BGSEN consists of the forward and the backward network. Based on the idea of inversely using the control tag generated by Padmanabhan's algorithm, Chen et al. proposed a routing algorithm for the backward network. Recently, Chen and Lou also proposed a routing algorithm for the backward network. It should be noted, however, that Padmanabhan's algorithm is actually an explicit formula for computing the control tag for routing and takes only O(1) time. Neither the algorithm of Chen et al. nor the algorithm of Chen and Lou provides an explicit formula for computing the control tag for routing and both algorithms take at least ω(n) time, where n + 1 is the number of stages in the BGSEN. This paper attempts to propose an explicit formula for computing the control tag for routing in the backward network. We will demonstrate how this formula greatly simplifies the computation process and how it leads to efficient routing algorithms. In particular, an O(1)-time one-to-one routing algorithm and an efficient routing-table construction algorithm have been proposed.