Revisiting Hamiltonian Decomposition of the Hypercube

A hypercube or binary n-cube is an interconnection network very suitable for implementing computing elements. In this paper we study the Hamiltonian decomposition, i.e. the partitioning of its edge set into Hamiltonian cycles. It is known that there are [n/2] disjoint Hamiltonian cycles on a binary...

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Vydáno v:13th Symposium on Integrated Circuits and Systems Design : proceedings : 18-24 September 2000, Manaus, Brazil s. 55
Hlavní autoři: Okuda, K., Song, S. W.
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: Washington, DC, USA IEEE Computer Society 18.09.2000
Edice:ACM Conferences
Témata:
Mathematics of computing
Mathematics of computing > Discrete mathematics
Mathematics of computing > Discrete mathematics > Combinatorics
Mathematics of computing > Discrete mathematics > Combinatorics > Combinatorial algorithms
Mathematics of computing > Discrete mathematics > Graph theory
Mathematics of computing > Discrete mathematics > Graph theory > Network flows
hypercube
disjoint Hamiltonian cycles
interconnection network
Hamiltonian decomposition
edge set
binary n-cube
hypercube networks
merge operator
graph colouring
ISBN:076950843X, 9780769508436
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Shrnutí:A hypercube or binary n-cube is an interconnection network very suitable for implementing computing elements. In this paper we study the Hamiltonian decomposition, i.e. the partitioning of its edge set into Hamiltonian cycles. It is known that there are [n/2] disjoint Hamiltonian cycles on a binary n-cube. The proof of this result, however, does not give rise to any simple construction algorithm of such cycles. In a previous work Song [1995] presented ideas towards a simple method to this problem. First decompose the hypercube into cycles of length 16, C/sub 16/, and then apply a merge operator to join the C/sub 16/ cycles into larger Hamiltonian cycles. The case of dimension n=6 (a 64-node hypercube) is illustrated. He conjectures the method can be generalized for any even n. In this paper, we generalize the first phase of that method for any even n and prove its correctness. Also we show four possible merge operators for the case of n=8 (a 256-node hypercube). This result can be viewed as a step toward the general merge operator, thus proving the conjecture.
Bibliografie:SourceType-Conference Papers & Proceedings-1
ObjectType-Conference Paper-1
content type line 25
ISBN:076950843X
9780769508436
DOI:10.5555/827245.827332