Bounding Work and Communication in Robust Cooperative Computation

Abstract

We consider the Do-All problem: p failure-prone processors perform t similar and independent tasks. We assume that processors are synchronous, communicate by message passing, and are subject to crashes determined by an adaptive adversary restricted only by the upper bound f on the number of crashes. The performance of algorithms in this setting is normally measured in terms of work (total available processor steps) and communication (total number of point-to-point messages) complexity. We consider work and communication as comparable resources and we develop algorithms that have efficient effort defined as work + communication. We present a p-processor, t-task algorithm that has effort \( \mathcal{O}(t + p^{1.77} ) \), against the unbounded adversary (p < p). This is the first algorithm that achieves subquadratic in p effort efficiency for unbounded adversary, or even for linearly-bounded adversary that crashes up to a constant fraction of the processors. We present another algorithm that has work \( \mathcal{O}(t + p\log ^2 p) \) against f-bounded adversaries such that p - f = Ω(p b) for a constant b, 0 < b < 1. We show how to achieve effort \( \mathcal{O}(t + p\log ^2 p) \) against a linearly-bounded adversary; this result is close to lower bound Ω(t + p log p/log logp).KeywordsNode DegreeFailure PatternDeterministic AlgorithmCommunication GraphMessage ComplexityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.