Fault tolerant algorithms are presented for broadcasting on the star graph. In our algorithm, fault tolerance is achieved by constructing an isomorphism of the star network, such that the faulty nodes minimally disrupt the message passing sequence. It is shown that, in the presence of r(1/spl les/r/spl les/k-2) faults, at most r extra steps are required by our algorithm to perform a one-to-all broadcasting in the k-star network. Our algorithm has the same time complexity as an optimal broadcasting algorithm, and, since it takes advantage of the hierarchical nature of the star graph network, it can be implemented easily. Our algorithm can also be used to perform all-to-all broadcasting in a faulty star graph.

In this paper, we design a new class of self-testing checkers, self-testing nonincreasing order checkers, for the first time. The self-testing nonincreasing order checker is a critical component to design concurrent checking VLSI sorters because it is capable of checking whether an arbitrary long sequence of numbers has been sorted, as well as testing itself during normal system operation.