Determining the conditional diagnosability of k-ary n-cubes under the MM* model

  • Authors:
  • Sun-Yuan Hsieh;Chi-Ya Kao

  • Affiliations:
  • Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan

  • Venue:
  • SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
  • Year:
  • 2011

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Abstract

Processor fault diagnosis plays an important role for measuring the reliability of multiprocessor systems, and the diagnosability of many well-known interconnection networks has been investigated widely. Conditional diagnosability is a novel measure of diagnosability, which is introduced by Lai et al., by adding an additional condition that any faulty set cannot contain all the neighbors of any vertex in a system. The class of k-ary n-cubes contains as special cases many topologies important to parallel processing, such as rings, hypercubes, and tori. In this paper, we study some topological properties of the k-ary n-cube, denoted by Qnk. Then we apply them to show that the conditional diagnosability of Qnk under the comparison diagnosis model is tc(Qnk) = 6n-5 for k ≥ 4 and n ≥ 4.