Scheduling Out-Trees Online to Optimize Maximum Flow

Kunal Agrawal, Benjamin Moseley, Heather Newman, Kirk Pruhs

Abstract: We consider online scheduling. on m identical processors. Jobs are parallel programs constructed using dynamic multithreading (also called fork-join parallelism). Jobs arrive over time online and the goal is to optimize maximum flow. Essentially all prior work on this problem has used a relaxed form of analysis where the algorithm has faster speed processors than the optimum and this paper seeks to understand the problem without this strong assumption. We show that the most natural algorithm, First-In-First-Out (FIFO), is Ømega(łog m)-competitive for jobs that are out-trees. For this challenging class where jobs are out-trees, we give new clairvoyant algorithm that is O(1)-competitive. We then give some circumstantial evidence that FIFO is O(łog m)-competitive, even on arbitrary jobs.