Publication details for Professor Iain StewartStewart, I.A. (2007). Distributed algorithms for building Hamiltonian cycles in k-ary n-cubes and hypercubes with faulty links. Journal of Interconnection Networks 8(3): 253-284.
- Publication type: Journal Article
- ISSN/ISBN: 0219-2659
- DOI: 10.1142/S0219265907002016
- Keywords: interconnection networks; k-ary n-cubes; hypercubes; fault-tolerance; Hamiltonian cycles; distributed algorithms; embeddings
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
We derive a sequential algorithm Find-Ham-Cycle with the following property. On input: k and n (specifying the k-ary n-cube Q(n,k); F, a set of at most 2n-2 faulty links; and v, a node of Q(n,k), the algorithm outputs nodes v+ and v- such that if Find-Ham-Cycle is executed once for every node v of Q(n,k) then the node v+ (resp. v-) denotes the successor (resp. predecessor) node of v on a fixed Hamiltonian cycle in Q(n,k) in which no link is in F. Moreover, the algorithm Find-Ham-Cycle runs in time polynomial in n and log k. We also obtain a similar algorithm for an n-dimensional hypercube with at most n-2 faulty links. We use our algorithms to obtain distributed algorithms to embed Hamiltonian cycles k-ary n-cubes and hypercubes with faulty links; our hypercube algorithm improves on a recently-derived algorithm due to Leu and Kuo, and our k-ary n-cube algorithm is the first distributed algorithm for embedding a Hamiltonian cycle in a k-ary n-cube with faulty links.
An extended abstract of this paper appeared in: Proc. of 12th International Conference on Parallel and Distributed Systems (ICPADS 2006), IEEE Computer Society Press (2006) 308-318.