Randomized registers and iterative algorithms

Abstract.We present three different specifications of a read-write register that may occasionally return out-of-date values - namely, a (basic) random register, a P-random register, and a monotone random register. We show that these specifications are implemented by the probabilistic quorum algorithm of Malkhi, Reiter, Wool, and Wright, and we illustrate how to program with such registers in the framework of Bertsekas, using the notation of Üresin and Dubois. Consequently, existing iterative algorithms for a significant class of problems (including solving systems of linear equations, finding shortest paths, constraint satisfaction, and transitive closure) will converge with high probability if executed in a system in which the shared data is implemented with registers satisfying the new specifications. Furthermore, the algorithms in this framework will inherit positive attributes concerning load and fault-tolerance from the underlying register implementation. The expected convergence time for iterative algorithms using the monotone implementation is analyzed and shown experimentally to improve on that of the original implementation. The message complexity for iterative algorithms using the monotone probabilistic quorum implementation is shown to improve on that of non-probabilistic implementations in a quantifiable situation.