The Conditional Fault-Diameter of the K-ary n-Cube
We obtain the conditional fault diameter of the k-ary n-cube interconnection network. It has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2005-06-01
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| Series: | Sultan Qaboos University Journal for Science |
| Subjects: | |
| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/332 |
| Summary: | We obtain the conditional fault diameter of the k-ary n-cube interconnection network. It has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. We extend this result by showing that the conditional fault-diameter of the k-ary n-cube is equal to the fault-free diameter plus two. This means that if there are at most 4n-3 faulty nodes in the k-ary n-cube and if every non-faulty node has at least one non-faulty neighbor, then there exists a fault-free path of length at most the diameter plus two between any two non faulty nodes. We also show how to construct these fault-free paths. With this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault diameter has been shown to be only two units over the fault-free diameter. |
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| ISSN: | 1027-524X 2414-536X |