Subscribe
Issue No.09 - September (1998 vol.9)
pp: 923-928
ABSTRACT
<p><b>Abstract</b>—The recently introduced interconnection networks, the Möbius cubes, are hypercube variants that have some better properties than hypercubes. The <it>n</it>-dimensional Möbius cube <it>M</it><sub><it>n</it></sub> is a regular graph with 2<super><it>n</it></super> nodes and <it>n</it>2<super><it>n</it>−1</super> edges. The diameter of <it>M</it><sub><it>n</it></sub> is about one half that of the <it>n</it>-dimensional hypercube <it>Q</it><sub><it>n</it></sub> and the average number of steps between nodes for <it>M</it><sub><it>n</it></sub> is about two-thirds of the average for <it>Q</it><sub><it>n</it></sub>, and 1 <tmath>$-$</tmath><it>M</it><sub><it>n</it></sub> has dynamic performance superior to that of <it>Q</it><sub><it>n</it></sub> [<ref rid="bibl09231" type="bib">1</ref>]. Of course, the symmetry of <it>M</it><sub><it>n</it></sub> is not superior to that of <it>Q</it><sub><it>n</it></sub>, i.e., <it>Q</it><sub><it>n</it></sub> is both node symmetric and edge symmetric [<ref rid="bibl092311" type="bib">11</ref>], whereas <it>M</it><sub><it>n</it></sub> is, in general, neither node symmetric (<it>n</it>≥ 4) nor edge symmetric (<it>n</it>≥ 3) [<ref rid="bibl09231" type="bib">1</ref>]. In this paper, we study the diagnosability of <it>M</it><sub><it>n</it></sub>. We use two diagnosis strategies, both based on the so-called PMC diagnostic model—the precise (one-step) diagnosis strategy proposed by Preparata et al. [<ref rid="bibl092310" type="bib">10</ref>] and the pessimistic diagnosis strategy proposed by Friedman [<ref rid="bibl09239" type="bib">9</ref>]. We show that the diagnosability of <it>M</it><sub><it>n</it></sub> is the same as that of <it>Q</it><sub><it>n</it></sub>, i.e., <it>M</it><sub><it>n</it></sub> is <it>n</it>-diagnosable under the precise diagnosis strategy and (2<it>n</it><tmath>$-$</tmath> 2)/(2<it>n</it><tmath>$-$</tmath> 2)-diagnosable under the pessimistic diagnosis strategy.</p>
INDEX TERMS
The Möbius cube, diagnosis, diagnosability, hypercube, multiprocessor system.
CITATION
Jianxi Fan, "Diagnosability of the Möbius Cubes", IEEE Transactions on Parallel & Distributed Systems, vol.9, no. 9, pp. 923-928, September 1998, doi:10.1109/71.722224