An Improved Characterization of I-step Re Overable Embeddings: Rings in Hypercubes
نویسنده
چکیده
An embedding is I-step recoverable ifany single fault occurs, the embedding can be reconfigured in one reconfiguration step to maintain the structure of the embedded graph. In this paper we present an efJicient scheme to construct this type of I -step recoverable ring embeddings in the hypercube. Our scheme will guarantee finding a I-step recoverable embedding of a length-k (even) ring in a d-cube where 6 2 k 2 (3/4)2d and d 2 3, provided such an embedding exists. Unlike previously proposed schemes, we solve the general problem of embedding rings of different lengths, and the resulting embeddings are of smaller expansion than in previous proposals. A suficient condition for the non-existence of I-step recoverable embeddings of rings of length > (3/4)2d in d-cubes is also given.
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