Fault tolerance in bubble-sort graph networks

  • Authors:

  • Shiying Wang;Yuxing Yang

  • Affiliations:

  • School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, PR China and School of Computer and Information Engineering, Anyang Normal University, Anyang, Henan 45500 ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

The bubble-sort graph B"n is one of the attractive underlying topologies for distributed systems. F"B(n,k) (resp. f"B(n,k)) is the minimum number of faulty nodes (resp. links) that make every (n-k)-dimensional sub-bubble-sort graph faulty in B"n under node (resp. link) failure model. In this paper, we proved that F"B(n,0)=f"B(n,0)=1, F"B(n,1)=f"B(n,1)=n for n=4, F"B(n,2)@?f"B(n,2)@?n(2n-3) for n=6, F"B(n,n-2)=n!/2 for n=3, f"B(n,n-2)=(n-1)n!/2 for n=3, F"B(n,n-1)=n! for n=2, and F"B(n,k)@?f"B(n,k)@?@?(k+1)/2@?k!C"k^n for n=6 and 3@?k@?n-3.