Fault-tolerance of Complete Josephus Cubes

  • Authors:
  • Peter K. K. Loh;W. J. Hsu

  • Affiliations:
  • Division of Computing Systems, School of Applied Science, Nanyang Technological University, Blk N4, #2A-32, Nanyang Avenue, Singapore 639798, Singapore;Division of Computing Systems, School of Applied Science, Nanyang Technological University, Blk N4, #2A-32, Nanyang Avenue, Singapore 639798, Singapore

  • Venue:
  • Journal of Systems Architecture: the EUROMICRO Journal
  • Year:
  • 2003

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Abstract

The Complete Josephus Cube is proposed as a fault-tolerant node cluster architecture A reliable and cost-effective communications strategy is also presented. For a Complete Josephus Cube of dimension r, the strategy tolerates up to (r + 1) encountered faults in its routes that are deadlock-free and livelock-free. The message is optimally (respectively, sub-optimally) delivered in at most r (respectively, 2r + 1) hops. Message overhead is one of the lowest reported for the specified fault tolerance--with only a single (r + 2)-bit routing vector accompanying the message to be communicated. Associated routing hardware may be implemented with standard logic.