@MISC{_performingwork, author = {}, title = {Performing Work in Broadcast Networks ∗}, year = {} }

Share

OpenURL

Abstract

We consider the problem of how to schedule t similar and independent tasks to be performed in a synchronous distributed system of p stations communicating via multipleaccess channels. Stations are prone to crashes whose patterns of occurrence are specified by adversarial models. Work, defined as the number of the available processor steps, is the complexity measure. We consider only reliable algorithms that perform all the tasks as long as at least one station remains operational. It is shown that every reliable algorithm has to perform work Ω(t + p √ t) even when no failures occur. An optimal deterministic algorithm for the channel with collision detection is developed, which performs only work O(t + p √ t). Another algorithm, for the channel without collision detection, performs work O(t + p √ t + p · min{f, t}), where f < p is the number of failures. This algorithm is proved to be optimal if upper bound f on the number of faults is the only restriction on the adversary. Finally, we consider the question if randomization helps against weaker adversaries for the channel without collision detection. A randomized algorithm is developed which performs only the expected minimum amount O(t + p √ t) of work, if the adversary may fail a constant fraction of stations only and it has to select failure-prone stations prior to the start of an execution. Key words: distributed algorithm, multiple-access channel, fail-stop failure, adversary, work, lower bound, independent tasks.