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DOI: 10.7155/jgaa.00061
Hamilton Decompositions and (n/2)-Factorizations of Hypercubes
Vol. 7, no. 1, pp. 79-98, 2003. Regular paper.
Abstract Since Qn, the hypercube of dimension n, is known to have n
link-disjoint 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.
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Submitted: November 2001.
Revised: September 2002.
Revised: February 2003.
Communicated by
Balaji Raghavachari
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