Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees Under the Comparison Diagnosis Model

Abstract

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 *This work was supported in part by the National Science Council of the Republic of China under Contract NSC 95-2221-E-009-134-MY3. 83 J. Inter. Net. 2008.09:83-97. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 08/16/15. For personal use only. 84 C.-K. Lin et al. the n-dimensional star graph S n 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 of alternating group networks

“…Cheng and Lipták [22] further generalized this result to star graphs with linearly many faults. Moreover, in terms of the size of connected components, Hsu et al [14] and Lin et al [13] also showed the conditional diagnosabilities for hypercube and star graphs, respectively. In this paper, based on the fault tolerance of alternating group networks AN n , we establish the conditional diagnosability of alternating group graphs AN n (n 5) under the comparison diagnosis model.…”

“…Zheng et al [12] analyzed the diagnosability of star graph under a comparison diagnostic model. Moreover, Lin et al [13] introduced the so-called conditional diagnosis, and showed that the conditional diagnosability of a star graph of size n is 3n − 7, which is about three times larger 0020-0190/$ -see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.ipl.2010.03.010 that the classical diagnosability of a star graph. In particular, Hsu et al [14] proved that the conditional diagnosability of a hypercube of size n is 3n − 5, based on the idea of Lai et al [15] who was the first to use a restricted diagnosis strategy.…”

Conditional Diagnosability of Complete Josephus Cubes

“…Lin et al [8] introduced the so-called conditional diagnosability of a system under the situation that no set of faulty vertices can contain all neighbors of any vertex in the system. A faulty set …”

“…Sengupta and Dahbura [12] developed this comparison approach such that the comparisons have no central unit involved. Lin et al [8] introduced the conditional diagnosis under the comparison model. By evaluating the size of connected components, they obtained that the conditional diagnosability of Star graph S n is 3n − 7.…”

An approach to conditional diagnosability analysis under the PMC model and its application to torus networks

“…Upon the receipt of the two responses, the processor compares them and proclaims that the two neighbors are both fault-free or at least one of them is faulty. Conditional diagnosability for interconnection networks under the MM model has been investigated in various studies [6,11,12,13,14,16,19,25,26].…”