Embedding of meshes in Mobius cubes
The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. Mobius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices. In this paper, we consider embedding of meshes in Mobius cubes. The main results obtained in this paper are: (1) For n >= 1, there exists a 2 x 2(n-1) mesh that can be embedded in the n-dimensional Mobius cube with dilation 1 and expansion 1. (2) For n >= 4, there exists a 4 x 2(n-2) mesh that can be embedded in the n-dimensional Mobius cube with dilation 2 and expansion 1. (3) For n >= 4, there are two disjoint 4 x 2(n-3) meshes that can be embedded in the 0-type n-dimensional Mobius cube with dilation 1. (4) For n >= 4, there are two disjoint 4 x 2(n-3) meshes that can be embedded in the 1-type n-climensional Mobius cube with dilation 2. Results of (1) and (3) are optimal in the sense that the dilations of the embeddings are 1. (c) 2008 Elsevier B.V. All rights reserved.
mobius cubes interconnection network dilation expansion mesh embedding