Symmetric k-factorizations of hypercubes with factors of small diameter

Abstract

The links of the hypercube Q/sub n/ can be partitioned into multiple link-disjoint spanning subnetworks, or factors. Each of these factors could simulate Q/sub n/. We therefore identify k-factorizations, or partitions of the links of Q/sub n/ into factors of degree k, where (1) the factorization exists for all values of n such that n mod k=0, (2) k is as small as possible, (3) the n/k factors have a similar structure, (4) the factors have as small a diameter as possible, and (5) the factors host Q/sub n/ with as small a dilation as possible. In this paper, we give an (n/2)-factorization of Q/sub n/, where n is even, generated by variations on reduced and thin hypercubes. The two factors are isomorphic, and both of the factors have diameter n+2. The diameter is an improvement over the best result known. Both of the factors also host Q/sub n/ with /spl Theta/(1) dilation.