Performing tasks on restartable message-passing processors

Abstract

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 f < p stop-failures and it does not allow restarts. It has the available processor steps complexity S = O((t + plog p/ log log p) · log f) and the message complexity M = O(t + plog p/ log log p + f · 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 S = O((t + plog p + f) · min{log p, log f}), and its message complexity is M = O(t + p · log p + f · p), where f is the number of failures.

This work was supported by the following contracts: ARPA N00014-92-J-4033 and F19628-95-C-0118, NSF 922124-CCR, ONR-AFOSR F49620-94-1-01997, and DFG-Graduiertenkolleg “Parallele Rechnernetzwerke in der Produktionstechnik” ME 872/4-1, DFG-SFB 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen”. The research of the third author was substantially done at the Massachusetts Institute of Technology. The research of the first and the third authors was partly done while visiting Heinz Nixdorf Institut, Universität-GH Paderborn.