Performing tasks on restartable Message–Passing processors

This work presents new algorithms for the “Do-All” problem that consists of performing t tasks reliably in a message-passing synchronous system of p fault-prone processors. The algorithms are based on an aggressive coordination paradigm in which multiple coordinators may be active as the result of failures. The first algorithm is tolerant of/< p stop-failures and it does not allow restarts. It has the available processor steps complexity S = 0((t+ plogp/log log p)–log f) and the message complexity M = 0(t + plogp/loglogp +/• p). Unlike prior solutions, our algorithm uses redundant broadcasts when encountering failures and, for large f, it has better S complexity. This algorithm is used as the basis for another algorithm which tolerates any pattern of stop-failures and restarts. This new algorithm is the first solution for the Do-All problem that efficiently deals with processor restarts. Its available processor steps complexity is 5 = 0((t+ p log p + f) -min{log p,log f}), and its message complexity is M = 0(t + p- logp +/-p), where/is the number of failures.