Issue No. 03 - March (2008 vol. 19)
We study the embedding of Hamiltonian cycle in the Crossed Cube, a prominent variant of the classical hypercube, which is obtained by crossing some straight links of a hypercube, and has been attracting much research interest in literatures since its proposal. We will show that due to the loss of link-topology regularity, generating Hamiltonian cycles in a crossed cube is a more complicated procedure than in its original counterpart. The paper studies how the crossed links affect an otherwise succinct process to generate a host of well-structured Hamiltonian cycles traversing all nodes. The condition for generating these Hamiltonian cycles in a crossed cube is proposed. An algorithm is presented that works out a Hamiltonian cycle for a given link permutation. The useful properties revealed and algorithm proposed in this paper can find their way when system designers evaluate a candidate network' s competence and suitability, balancing regularity and other performance criteria, in choosing an interconnection network.
Crossed cube, Embedding, Hamiltonian cycles, Interconnection architectures, Network topology
D. Wang, "On Embedding Hamiltonian Cycles in Crossed Cubes," in IEEE Transactions on Parallel & Distributed Systems, vol. 19, no. , pp. 334-346, 2007.