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<p><b>Abstract</b>—In this note, we use a vertex-isoperimetric inequality to show that the number of test and repair iterations needed to perform sequential diagnosis of <it>d</it>-dimensional hypercubes is upper bounded by <tmath>d-r</tmath>, where <tmath>r\in\Theta(d)</tmath>. This result improves the best bound of <it>d</it> test and repair iterations previously known. Numerical evaluation has shown that the actual value of <it>r</it> ranges from 0.16<it>d</it> to 0.31<it>d</it>.</p>
Massively parallel systems, system-level diagnosis, sequential diagnosis, hypercubes.
Paolo Santi, Stefano Chessa, "Reducing the Number of Sequential Diagnosis Iterations in Hypercubes", IEEE Transactions on Computers, vol. 53, no. , pp. 89-92, January 2004, doi:10.1109/TC.2004.1255796
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