Abstract
In this work, we study the problem of scheduling parallelizable jobs online with an objective of minimizing average flow time. Each parallel job is modeled as a DAG where each node is a sequential task and each edge represents dependence between tasks. Previous work has focused on a model of parallelizability known as the arbitrary speed-up curves setting where a scalable algorithm is known. However, the DAG model is more widely used by practitioners, since many jobs generated from parallel programming languages and libraries can be represented in this model. However, little is known for this model in the online setting with multiple jobs. The DAG model and the speed-up curve models are incomparable and algorithmic results from one do not immediately imply results for the other. Previous work has left open the question of whether an online algorithm can be O(1)-competitive with O(1)-speed for average flow time in the DAG setting. In this work, we answer this question positively by giving a scalable algorithm which is (1 + e)-speed O([EQUATION])-competitive for any e > 0. We further introduce the first greedy algorithm for scheduling parallelizable jobs --- our algorithm is a generalization of the shortest jobs first algorithm. Greedy algorithms are among the most useful in practice due to their simplicity. We show that this algorithm is (2 + e)-speed O([EQUATION])-competitive for any e > 0.
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