A Boolean Expression-Based Approach for Maximum Incomplete Subcube Identification in Faulty Hypercubes

An incomplete hypercube possesses virtually every advantage of complete hypercubes, including simple deadlock-free routing, a small diameter, bounded link traffic density, a good support of parallel algorithms, and so on. It is natural to reconfigure a faulty hypercube into a maximum incomplete cube so as to lower potential performance degradation, because a hypercube so reconfigured often results in a much larger system than what is attainable according to any conventional reconfiguration scheme which identifies only complete subcubes. A maximum incomplete subcube involves one maximum complete subcube, plus certain smaller complete subcubes, and, thus, may accommodate multiple jobs of different sizes simultaneously, delivering a higher performance level. This paper proposes an efficient approach for identifying all the maximum incomplete subcubes present in a faulty hypercube. The proposed approach is on the basis of manipulating Boolean expressions, with the search space reduced considerably by taking advantage of the basic properties of faulty hypercubes during expression manipulation. It is distributed, in that every healthy node executes the same identification algorithm independently, at the same time, it is confirmed by fault simulation that our approach indeed gives rise to significantly larger reconfigured systems and requires short execution times.