Work-Competitive Scheduling on Task Dependency Graphs

Abstract

A fundamental problem in distributed computing is the task of cooperatively executing a given set of [Formula: see text] tasks by [Formula: see text] asynchronous processors where the communication medium is dynamic and subject to failures. Also known as do-all, this problem been studied extensively in various distributed settings. In [2], the authors consider a partitionable network scenario and analyze the competitive performance of a randomized scheduling algorithm for the case where the tasks to be completed are independent of each other. In this paper, we study a natural extension of this problem where the tasks have dependencies among them. We present a simple randomized algorithm for [Formula: see text] processors cooperating to perform [Formula: see text] known tasks where the dependencies between them are defined by a [Formula: see text]-partite task dependency graph and additionally these processors are subject to a dynamic communication medium. By virtue of the problem setting, we pursue competitive analysis where the performance of our algorithm is measured against that of the omniscient offline algorithm which has complete knowledge of the dynamics of the communication medium. We show that the competitive ratio of our algorithm is tight and depends on the dynamics of the communication medium viz. the computational width defined in [2] and also on the number of partitions of the task dependency graph.