Symmetric k-factorizations of hypercubes with factors of small diameter

Abstract

The links of the hypercube Q n can be partitioned into multiple link-disjoint spanning subnetworks, or factors. Each of these factors could simulate Q n . We therefore identify k-factorizations, or partitions of the links of Q 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 n with as small a dilation as possible.In this paper, we give an (n/2)-factorization of Q 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 n with Θ(1) dilation.

Hamilton Decompositions and (n/2)-Factorizations of Hypercubes

“…We use the idea behind reduced and thin hypercubes, to construct an (n/2)-factorization of Q n , where n is even, where the factors have diameter n + Θ(1). This factorization was first given in [9]. Consider Q n , where n is even.…”