Subcube Determination in Faulty Hypercubes

A hypercube may operate in a gracefully degraded manner, after faults arise, by supporting the execution of parallel algorithms in smaller fault-free subcubes. In order to reduce execution slowdown in a hypercube with given faults, it is essential to identify the maximum healthy subcubes in the faulty hypercube because the time for executing a parallel algorithm tends to depend on the dimension of the assigned subcube. This paper describes an efficient procedure capable of determining all maximum faultfree subcubes in a faulty hypercube. The procedure is a distributed one, since every healthy node next to a failed component performs the same procedure independently and concurrently. Based on interesting properties of faulty hypercubes, this procedure exhibits empirically polynomial time complexity with respect to the system dimension and the number of faults, for a practical range of dimensions. It compares favorably with prior methods when the number of faults is in the order of the system dimension. This procedure can deal with node failures and link failures uniformly and equally efficiently.