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2005

A note on edge fault tolerance with respect to hypercubes

8 years 9 months ago
A note on edge fault tolerance with respect to hypercubes
In the previous studies on k-edge fault tolerance with respect to hypercubes Qn, matrices for generating linear k-EFT(Qn) graphs were used. Let EFTL(n, k) denote the set of matrices that generate linear k-EFT(Qn) graphs. A matrix in EFTL(n, k) with the smallest number of rows among all matrices in EFTL(n, k) is optimal. We use eftL(n, k) to denote the difference between the number of rows and the number of columns in any optimal EFTL(n, k) matrix. In terms of Hamming weight, in this work we present a necessary and sufficient condition for those matrices in EFTL(n, k) and another necessary and sufficient condition for those matrices in EFTL(n, k) of the form In D . We also prove that eftL(n, k + 1) eftL(n, k) + 1 and that eftL(n, k + 1) = eftL(n, k) + 1 if k is even.
Tung-Yang Ho, Ting-Yi Sung, Lih-Hsing Hsu
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2005
Where APPML
Authors Tung-Yang Ho, Ting-Yi Sung, Lih-Hsing Hsu
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