Scheduling algorithms for workflow optimization

Pipelined workflows are a popular programming paradigm for parallel applications. In these workflows, the computation is divided into several stages and these stages are connected to each other through first-in first-out channels. In order to execute these workflows on a parallel machine, we must first determine the mapping of the stages onto the various processors on the machine. After finding the mapping, we must compute the schedule — the order in which the various stages execute on their assigned processors. In this paper, we explore the scheduling problem for linear workflows, assuming that the mapping is given. Linear workflows are a special case of workflows for which the dependencies between stages can be represented by a linear graph. The objective of the scheduling algorithm is either to maximize throughput or to minimize latency or both. We consider two realistic execution models: the one-port model and the multi-port model. In both models, finding a schedule to minimize latency is easy. However, computing the schedule to minimize period (maximize throughput) is NP-hard in the one-port model, but can be done in polynomial time in the multi-port model. We also present an approximation algorithm to minimize period in the one-port model. Finally, the bi-criteria problem, which consists in finding a schedule respecting a given period and a given latency, is NP-hard in both models.