Fault tolerance in k-ary n-cube networks

Authors:
Shiying Wang;Guozhen Zhang;Kai Feng
Affiliations:
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, PR China
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

The k-ary n-cube Q"n^k is one of the most commonly used interconnection topologies for parallel and distributed computing systems. Let f(n,m) be the minimum number of faulty nodes that make every (n-m)-dimensional subcube Q"n"-"m^k faulty in Q"n^k under node-failure models. In this paper, we prove that f(n,0)=1, f(n,1)=k for odd k=3, f(n,n-1)=k^n^-^1 for odd k=3, and k^m@?f(n,m)@?(n-1m-1)k^m-(n-2m-1)k^m^-^1 for odd k=3.