Uniform Disjoint Cycle Covers on a Hierarchical Multicomputer System

Abstract

The hypercube has been widely used as the interconnection network in parallel computers. The crossed cube is an variation of hypercube and preserves many of its desirable properties. The hierarchical crossed cube draws upon constructions used within the hypercube and also the crossed cube and is suitable for massively parallel systems with thousands of processors and owns many alluring features, such as symmetry and logarithmic diameter. Embedding cycles into interconnection networks is an important issue for the design of interconnection networks and cycle covering is a well-studied problem in computer science. In this paper, we propose a scheme for a variant of cycle covering problem in hierarchical crossed cubes which all cycles have the same length and each cycle contains the same number of vertices in each crossed cube. Furthermore, we obtain a lower bound for the number of uniform disjoint cycle covers in hierarchical crossed cubes.