Fault tolerant broadcasting in SIMD hypercubes

In this paper, we propose an optimal fault tolerant broadcasting algorithm which requires only n+1 steps for an SIMD hypercube, with up to n-1 faulty nodes. The basic idea of the proposed algorithm is first to find a fault-free subcube (C/sub s/) which contains the source node such that each neighboring subcube of the subcube C/sub s/ contains at least one fault. Next, the message is broadcast along the internal dimensions followed by external dimensions of the subcube C/sub s/. This process requires n steps. Since this process does not guarantee that all the fault-free nodes receive the message, an extra step may be needed. We prove that there exists an internal dimension of the subcube C/sub s/ such that all the nodes which did not receive the message in n steps will receive the message by broadcasting the message along that dimension. We also develop a generalized broadcasting algorithm which tolerates any number of faults.<<ETX>>