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Embedding Cube-Connected Cycles Graphs into Faulty Hypercubes
October 1994 (vol. 43 no. 10)
pp. 1210-1219

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults.

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Index Terms:
hypercube networks; fault tolerant computing; reliability; cube-connected cycles graphs embedding; faulty hypercubes; ascend-descend algorithms; bitonic sort; spanning torus.
J. Bruck, R. Cypher, D. Soroker, "Embedding Cube-Connected Cycles Graphs into Faulty Hypercubes," IEEE Transactions on Computers, vol. 43, no. 10, pp. 1210-1219, Oct. 1994, doi:10.1109/12.324546
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