Node set optimization problem for complete Josephus cubes

Abstract

The problem of finding an optimal node set in an interconnection network plays an important role in minimizing the layout of embedding the network into linear chassis. In this paper we find the nested optimal node sets for a complete Josephus cube, a recently proposed fault-tolerant node cluster architecture variant of the binary hypercube which has the same number of nodes as the hypercube but exhibits enhanced embedding, fault tolerance and communications performance than the hypercube and many of its variants. As a byproduct we obtain the minimum layout of embedding the complete Josephus cube into a path, 1-rooted complete binary tree, sibling tree and caterpillar.