2 research outputs found
Embedding cube-connected cycles graphs into faulty hypercubes
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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Partitioning and broadcasting in hypercubes in the presence of faulty communication links
The problem of broadcasting in faulty hypercubes is considered, based upon a strategy of partitioning the faulty hypercube into subcubes in which currently known algorithms can be implemented. Three similar partitioning and broadcasting algorithms for an n-dimensional hypercube in the presence of up to (n² + 2n - c) / 4 faulty communication links are presented, where c = 4 if n is an even number or c = 3 if n is an odd number. The most efficient algorithm is implemented in 1.3n + 6log(n) + 9 time units. To the best of our knowledge, this algorithm is the most efficient one for an n-dimensional hypercube in the presence of O(n²) faults