A Note on Diagnosability of Large Fault Sets on Star Graphs

Chen, Y-Chuang; Liu, Shun-Fu

doi:10.1109/tc.2010.234

Cited by 5 publications

(4 citation statements)

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“…In the current paper, with Lemmas 3.9-3.11, we have shown that Property 7 holds just for . Recently, Chen and Liu [5] found counterexamples to Property 7: First, they selected a 3-dimensional substar graph, say , of Star Graph . In fact, is exactly a cycle of length 6.…”

Section: -Diagnosability Of Star Graphsmentioning

confidence: 99%

“…Obviously, < a contradiction. However, [5] provided the counterexamples to Property 7 without further examining the cause that led to the flawed result. In the rest of this section, we pinpoint the missteps in the proof of Property 7 [26].…”

Section: -Diagnosability Of Star Graphsmentioning

confidence: 99%

“…But the rather informal proof in [26] for this proposition was later found flawed. Recently, Chen and Liu pointed out that the -diagnosability of is actually , and it only holds for a relatively small [5]. However, no specific range of was suggested in [5].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Chen and Liu pointed out that the -diagnosability of is actually , and it only holds for a relatively small [5]. However, no specific range of was suggested in [5]. To the best of our knowledge, no -diagnostic algorithms have been proposed for the Star Graphs in literature.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The $t/k$-Diagnosability of Star Graph Networks

Zhou

Lin

et al. 2015

IEEE Trans. Comput.

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The -diagnosis is a diagnostic strategy at system level that can significantly enhance the system's self-diagnosing capability. It can detect up to faulty processors (or nodes, units) which might include at most misdiagnosed processors, where is typically a small number. Somani and Peleg ([26], 1996) claimed that an -dimensional Star Graph (denoted ), a well-studied interconnection model for multiprocessor systems, is -diagnosable. Recently, Chen and Liu ([5], 2012) found counterexamples for the diagnosability obtained in [26], without further pursuing the cause of the flawed result. In this paper, we provide a new, complete proof that an -dimensional Star Graph is actually -diagnosable, where , and investigate the reason that caused the flawed result in [26]. Based on our newly obtained fault-tolerance properties, we will also outline an diagnostic algorithm ( is the number of nodes in ) to locate all (up to ) faulty processors, among which at most fault-free processors might be wrongly diagnosed as faulty.

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Section: -Diagnosability Of Star Graphsmentioning

confidence: 99%

Section: -Diagnosability Of Star Graphsmentioning

confidence: 99%