Since Qn, the hypercube of dimension n, is known to have n linkdisjoint paths between any two nodes, the links of Qn can be partitioned into multiple link-disjoint spanning subnetworks, or factors. We seek to identify factors which efficiently simulate Qn, while using only a portion of the links of Qn. We seek to identify (n/2)-factorizations, of Qn where 1) the factors have as small a diameter as possible, and 2) mappings (embeddings) of Qn to each of the factors exist, such that the maximum number of links in a factor corresponding to one link in Qn (dilation), is as small as possible. In this paper we consider two algorithms for generating Hamilton decompositions of Qn, and three methods for constructing (n/2)-factorizations of Qn for specific values of n. The most notable (n/2)factorization of Qn results in two mutually isomorphic factors, each with diameter n + 2, where an embedding exists which maps Qn to each of the factors with constant dilation.
Since Qn, the hypercube of dimension n, is known to have n linkdisjoint paths between any two nodes, the links of Qn can be partitioned into multiple link-disjoint spanning subnetworks, or factors. We seek to identify factors which efficiently simulate Qn, while using only a portion of the links of Qn. We seek to identify (n/2)-factorizations, of Qn where 1) the factors have as small a diameter as possible, and 2) mappings (embeddings) of Qn to each of the factors exist, such that the maximum number of links in a factor corresponding to one link in Qn (dilation), is as small as possible. In this paper we consider two algorithms for generating Hamilton decompositions of Qn, and three methods for constructing (n/2)-factorizations of Qn for specific values of n. The most notable (n/2)-factorization of Qn results in two mutually isomorphic factors, each with diameter n + 2, where an embedding exists which maps Qn to each of the factors with constant dilation.
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.
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