Diagnosability of Hypercubes and Enhanced Hypercubes under the Comparison Diagnosis Model

  • Authors:
  • Dajin Wang

  • Affiliations:
  • Montclair State Univ., Upper Montclair, NJ

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1999

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Abstract

In [10], Sengupta and Dahbura discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by Maeng and Malek [7] and a polynomial algorithm was given to identify the faulty processors provided that the system's diagnosability is known. However, for a general system, the determination of its diagnosability is not algorithmically easy. This paper proves that, for the important hypercube-structured multiprocessor systems ($n$-cubes), the diagnosability under the comparison model is $n$ when $n\geq 5$. The paper also studies the diagnosability of enhanced hypercube [11], which is obtained by adding $2^{n-1}$ more links to a regular hypercube of $2^{n}$ processors. It is shown that the augmented communication ability among processors also increases the system's diagnosability under the comparison model. We will prove that the diagnosability is $n+1$ for an enhanced hypercube when $n\geq 6$.