Tolerating a faulty edge in a multi-dimensional mesh
The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a mesh M, find a mesh G which satisfies the following conditions: (1) G and M have the same number of nodes, (2) for any subset of k edges in G,...
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Published in | Proceedings of Phoenix Conference on Computers and Communications pp. 9 - 15 |
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Main Author | |
Format | Conference Proceeding |
Language | English |
Published |
IEEE
1993
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Subjects | |
Online Access | Get full text |
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Summary: | The author examines the problem of tolerating faulty edges in the multidimensional mesh architecture. This problem can be briefly defined as follows. Given a mesh M, find a mesh G which satisfies the following conditions: (1) G and M have the same number of nodes, (2) for any subset of k edges in G, there is a submesh in G isomorphic to M which excludes these k edges, and (3) G has the least possible number of edges. The mesh G which satisfies these conditions is called a symmetrically optimal k-edge-fault-tolerant (k-EFT) extension of M. It is shown that, even when k=1, finding such a mesh G is a very difficult problem. A necessary and sufficient condition is developed for characterizing the class of symmetrically optimal 1-EFT extensions of any given mesh. Two new methods are proposed based on this characterization for finding symmetrically optimal, or symmetrically near-optimal, 1-EFT extensions. The first method finds an optimal solution, but is useful only for meshes whose number of dimensions is relatively small. The second method finds only a near optimal solution by decomposing a mesh with a large number of dimensions into several meshes with a smaller number of dimensions that can be solved by the first method.< > |
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ISBN: | 0780309227 9780780309227 |
DOI: | 10.1109/PCCC.1993.344491 |