DocumentCode :
11328
Title :
Conditional (t,k) -Diagnosis in Graphs by Using the Comparison Diagnosis Model
Author :
Chun-An Chen ; Guey-Yun Chang ; Sun-Yuan Hsieh
Author_Institution :
Dept. of Comput. Sci. & Inf. Eng., Nat. Cheng Kung Univ., Tainan, Taiwan
Volume :
64
Issue :
6
fYear :
2015
fDate :
June 1 2015
Firstpage :
1622
Lastpage :
1632
Abstract :
(t, k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors be identified and repaired in each iteration when there are at most t faulty processors, where t ≥ k. Based on the assumption that each vertex is adjacent to at least one fault-free vertex, the conditional (t, k)-diagnosis of graphs was investigated by using the comparison diagnosis model. Lower bounds on the conditional (t, k)-diagnosability of graphs were derived, and applied to obtain the following results. 1) Symmetric d-dimensional grids are conditionally (N/2d+1 -1, 2d -1)-diagnosable when d ≥ 2 and N (the number of vertices) ≥ 4d. 2) Symmetric d-dimensional tori are conditionally (1/5 (N + min{8/5 N2/3, 2N-20/15} - 2), 6)-diagnosable when d = 2 and N ≥ 49 and ( N/2d+1 -1, 4d-2)-diagnosable when d ≥ 3 and N ≤ 4d. 3) Cube-connected cycles are conditionally (N/4 - 1, 4)-diagnosable. 4) k-ary trees are conditionally (N/k+1 - 1)-diagnosable.
Keywords :
fault diagnosis; graph theory; multiprocessing systems; comparison diagnosis model; conditional (t, k)-diagnosis; cube-connected cycles; fault-free vertex; faulty processors; k-ary trees; lower bounds; multiprocessor systems; sequential diagnosis generalization; symmetric d-dimensional grids; symmetric d-dimensional tori; Circuit faults; Computational modeling; Educational institutions; Fault diagnosis; Multiprocessing systems; Program processors; Sequential diagnosis; Conditional fault diagnosis; MM* model; fault-tolerance; multiprocessor systems; sequential diagnosis; system-leveldiagnosis; t,k-diagnosis;
fLanguage :
English
Journal_Title :
Computers, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9340
Type :
jour
DOI :
10.1109/TC.2014.2345407
Filename :
6871331
Link To Document :
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