Tradeoffs in the design of efficient algorithm-based error detection schemes for hypercube multiprocessors

The authors provide an in-depth study of the various issues and tradeoffs available in algorithm-based error detection, as well as a general methodology for evaluating the schemes. They illustrate the approach on an extremely useful computation in the field of numerical linear algebra: QR factorization. They have implemented and investigated numerous ways of applying algorithm-based error detection using different system-level encoding strategies for QR factorization. Specifically, schemes based on the checksum and sum-of-squares (SOS) encoding techniques have been developed. The results of studies performed on a 16-processor Intel iPSC-2/D4/MX hypercube multiprocessor are reported. It is shown that, in general, the SOS approach gives much better coverage (85-100%) for QR factorization while maintaining low overheads (below 10%).>