On sequential diagnosis of multiprocessor systems

Discrete Applied Mathematics

2008

We consider problems of fault diagnosis in multiprocessor systems. Preparata, Metze and Chien [F.P. Preparata, G. Metze, R.T. Chien, On the connection assignment problem of diagnosable systems, IEEE Trans. Comput. EC 16 (12) (1967) 848-854] introduced a graph theoretical model for system-level diagnosis, in which processors perform tests on one another via links in the system. Fault-free processors correctly identify the status of tested processors, while the faulty processors can give arbitrary test results. The goal is to identify faulty processors based on the test results. A system is said to be t-diagnosable if faulty units can be identified, provided the number of faulty units present does not exceed t. We explore here diagnosis problems for n-cube systems and give bounds for diagnosability of the n-cube. We also describe a simple diagnosis algorithm A which is linear in time and which can be used for sequential diagnosis as well as for incomplete diagnosis in one step. In particular, the algorithm applied to arbitrary topology based interconnection systems G with N processors improves previously known ones. It has sequential diagnosability t A (G) ≥ 2N 1 2 − 3, which is optimal in the worst case.

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Section: Problemmentioning

confidence: 97%

On diagnosability of large multiprocessor networks

Discrete Applied Mathematics

2008

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“…Proof As noticed in [16], it is sufficient to prove the theorem for the case when n is a power of 2. Let n = 2 k and let B 1 , .…”

Section: Lemmamentioning

confidence: 99%

“…(ii) (Yamada et al [16]) Given integer n ≥ 3 we have m(H n ) ≥ n ⌊ n 2 ⌋ and hence the degree of sequential diagnosability of the n-cube t(H n ) > n ⌊ n 2 ⌋ An important parameter in sequential diagnosis is the number of tests and repair iterations needed to locate all the faulty units within the system (see [5], [15]). Thus, reducing the number of iterations is an important task in implementation of a diagnosis scheme.…”

Section: Lemmamentioning

confidence: 99%

“…Recently Yamada et al [16] improved the lower bound into t(n)= Ω (2 n / √ n), applying the result of Kleitman [10], which states that λ(n, 2 n−1 +1) ≥ n n/2 −1 and hence m(n) = Ω (2 n / √ n). They also obtained the upper bound t(n) = O 2 n log n √ n which greatly improves previously known ones.…”

Section: Introductionmentioning

confidence: 99%

“…They also obtained the upper bound t(n) = O 2 n log n √ n which greatly improves previously known ones. A sequential diagnosis algorithm (referred to as HYBRID) for arbitrary interconnection graphs G on N vertices was proposed in [16] …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On diagnosability of large multiprocessor networks

Electronic Notes in Discrete Mathematics

2005

We consider problems of fault diagnosis in multiprocessor systems. Preparata, Metze and Chien (1967) introduced a graph theoretical model for system-level diagnosis, in which processors perform tests on one another via links in the system. Faultfree processors correctly identify the status of tested processors, while the faulty processors can give arbitrary test results. The goal is to identify faulty processors based on the test results. A system is said to be t-diagnosable if faulty units can be identified, provided the number of faulty units present does not exceed t. We explore here diagnosis problems for n-cube systems and give bounds for diagnosability of the n-cube. We also describe a simple diagnosis algorithm A which is linear in time and which can be used for sequential diagnosis as well as for incomplete diagnosis in one step. In particular the algorithm applied to arbitrary topology based interconnection systems G with N processors improves previously known ones. It has sequential diagnosability t A (G) ≥ ⌈2N 1 2 ⌉ − 3, which is optimal in the worst case.

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Interactive Communication, Diagnosis and Error Control in Networks

Algorithmics of Large and Complex Networks

2009