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As more and more parallel programs are migrating to shared computing platforms, bounding their parallel execution times under resource constraints is particularly important for their efficient executions. The parallel program is often modeled as a task graph, which is composed of a collection of control or data-dependent sub-tasks organized as a directed acyclic graph (DAG) for scheduling. In this paper, we propose a simple yet effective method to bound the parallel execution time of a task graph when the memory resources are constrained. The essence of this method is to extend Brent’s theorem by incorporating the memory factor. To this end, we introduce a concept of range of concurrent tasks (RCT) and leverage it to estimate an upper bound on the parallel execution time of task graph with respect to work-conserving scheduling algorithm. And also we exploit the estimated bound to develop a metric to help determine optimal memory capacity for a given task graph. Through an empirical study, we evaluate how good the estimated bound is via a designed scheduling algorithm and demonstrate the effectiveness of the metric in the selection of optimal memory capacity for a task graph.

Toward Bounds on Parallel Execution Times of Task Graphs on Multicores With Memory Constraints