A New Tag Scheme and Its Tree Representation for a Shuffle-Exchange Network

Abstract

This paper introduces a new tag scheme having a flexibility and a bidirectionality for an N ¿ N k-stage shuffle-exchange network where k \ge log_2 N. Based on the interstage correlations for a path, the EB-tag generating rules are presented. In addition, an elegant and simple graphical representation called a N-leaf Dual Complete Binary tree (N-leaf DCB-tree) for a given permutation is proposed and its characteristics are discussed. Then the universal necessary condition for a conflict-free connection pattern is given. Due to this condition, the conflict-free routing problem can be transformed to the perfect assignment problem.