The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

Authors:
Behrooz Parhami
Affiliations:
Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Information Processing Letters
Year:
2005

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Abstract

A two-level swapped (also known as optical transpose interconnect system, or OTIS) network with n^2 nodes is built of n copies of an n-node basis network constituting its clusters. A simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j for all ij) leads to regularity, modularity, packageability, fault tolerance, and algorithmic efficiency of the resulting networks. We prove that a swapped network is Hamiltonian if its basis network is Hamiltonian. This general closure property for Hamiltonicity under swap or OTIS composition replaces a number of proofs in the literature for specific basis networks and obviates the need for proving Hamiltonicity for many other basis networks of potential practical interest.