Conditional diagnosability of multiprocessor systems based on complete-transposition graphs

In a multiprocessor system, as a key measure index for evaluating its reliability, diagnosability has attracted lots of attentions. Traditional diagnosability and conditional diagnosability have already been widely discussed. However, the existing diagnosability measures are not sufficiently comprehensive to address a large number of faulty nodes in a system. This article introduces a novel concept of diagnosability, called two-round diagnosability, which means that all faulty nodes can be identified by at most a one-round replacement (repairing the faulty nodes). The characterization of two-round t-diagnosable systems is provided; moreover, several important properties are also presented. Based on the abovementioned theories, for the n-dimensional hypercube Qn, we show that its two-round diagnosability is n2+n/2, which is n+1/2 times its classic diagnosability. Furthermore, a fault diagnosis algorithm is proposed to identify each node in the system under the PMC model. For Qn, we prove that the proposed algorithm is the time complexity of On2n.

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Strong Diagnosability and Conditional Diagnosability of Multiprocessor Systems and Folded Hypercubes

IEEE Transactions on Computers ◽

10.1109/tc.2012.110 ◽

2013 ◽

Vol 62 (7) ◽

pp. 1472-1477 ◽

Cited By ~ 42

Author(s):

Sun-Yuan Hsieh ◽

Cheng-Yen Tsai ◽

Chun-An Chen

Keyword(s):

Multiprocessor Systems ◽

Conditional Diagnosability

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CONDITIONAL DIAGNOSABILITY OF CAYLEY GRAPHS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS MODEL

Journal of Interconnection Networks ◽

10.1142/s0219265908002175 ◽

2008 ◽

Vol 09 (01n02) ◽

pp. 83-97 ◽

Cited By ~ 77

Author(s):

CHENG-KUAN LIN ◽

JIMMY J. M. TAN ◽

LIH-HSING HSU ◽

EDDIE CHENG ◽

LÁSZLÓ LIPTÁK

Keyword(s):

Cayley Graphs ◽

Multiprocessor Systems ◽

Star Graph ◽

Reliable Computing ◽

Star Graphs ◽

Comparison Model ◽

Diagnosis Model ◽

Conditional Diagnosability

The diagnosis of faulty processors plays an important role in multiprocessor systems for reliable computing, and the diagnosability of many well-known networks has been explored. Zheng et al. showed that the diagnosability of the n-dimensional star graph Sn is n - 1. Lai et al. introduced a restricted diagnosability of multiprocessor systems called conditional diagnosability. They consider the situation when no faulty set can contain all the neighbors of any vertex in the system. In this paper, we study the conditional diagnosability of Cayley graphs generated by transposition trees (which include the star graphs) under the comparison model, and show that it is 3n - 8 for n ≥ 4, except for the n-dimensional star graph, for which it is 3n - 7. Hence the conditional diagnosability of these graphs is about three times larger than their classical diagnosability.

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