Identification of operational subcubes in unreliable hypercubes

Abstract

Hypercube multiprocessors can efficiently execute a wide class of parallel algorithms. To obtain a reliable result, the correct operation of all processors in the network must be ensured. However, the number of processors in a hypercube network grows exponentially with the network dimension, making the network susceptible to node failures. Fortunately, most of the basic algorithms developed for networks such as the hypercube can be formulated with the dimension of the network as a parameter of the algorithm. Therefore it is essential to investigate methods to identify the operational subcubes (OPSCs) contained in a hypercube with some faulty node processors. The paper proposes centralised and distributed algorithms to identify OPSCs in an n-cube when the faulty processors are abundant. By utilising the properties of an unreliable environment, the proposed algorithms can identify all the largest OPSCs efficiently. Such algorithms are highly desirable since, in general, the problem of finding an OPSC in a damaged cube has an exponential time complexity.Methods are given to update the status of OPSCs dynamically once a working node fails or a faulty node is repaired.