Conditional diagnosability of multiprocessor systems based on Cayley graphs generated by transpositions

2021 ◽  
Vol 304 ◽  
pp. 137-152
Author(s):  
Mei-Mei Gu ◽  
Rong-Xia Hao ◽  
Yan-Quan Feng ◽  
Erling Wei
Keyword(s):  
Cayley Graphs ◽  
Multiprocessor Systems ◽  
Conditional Diagnosability

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

2008 ◽  
Vol 09 (01n02) ◽  
pp. 83-97 ◽  
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.

Conditional diagnosability measures for large multiprocessor systems

2005 ◽  
Vol 54 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Pao-Lien Lai ◽  
J.J.M. Tan ◽  
Chien-Ping Chang ◽  
Lih-Hsing Hsu
Keyword(s):  
Multiprocessor Systems ◽  
Conditional Diagnosability

scholarly journals Two-Round Diagnosability Measures for Multiprocessor Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jiarong Liang ◽  
Qian Zhang ◽  
Changzhen Li
Keyword(s):  
Fault Diagnosis ◽  
Time Complexity ◽  
Multiprocessor System ◽  
Multiprocessor Systems ◽  
Pmc Model ◽  
Diagnosis Algorithm ◽  
Conditional Diagnosability ◽  
Novel Concept ◽  
Measure Index

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.

A UNIFIED APPROACH TO THE CONDITIONAL DIAGNOSABILITY OF INTERCONNECTION NETWORKS

2012 ◽  
Vol 13 (03n04) ◽  
pp. 1250007 ◽  
Author(s):  
EDDIE CHENG ◽  
LÁSZLÓ LIPTÁK ◽  
KE QIU ◽  
ZHIZHANG SHEN
Keyword(s):  
Interconnection Networks ◽  
Ad Hoc ◽  
Cayley Graphs ◽  
Alternating Group ◽  
Unified Approach ◽  
Star Graphs ◽  
Conditional Diagnosability

The conditional diagnosability of interconnection networks has been studied in a number of ad-hoc methods resulting in various conditional diagnosability results. In this paper, we utilize these existing results to give an unified approach in studying this problem. Following this approach, we derive the exact value of the conditional diagnosability for a number of interconnection networks including Cayley graphs generated by 2-trees (which generalize alternating group graphs), arrangement graphs (which generalize star graphs and alternating group graphs), hyper Petersen networks, and dual-cube like networks (which generalize dual-cubes.)

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