Integrating Task Duplication in Optimal Task Scheduling With Communication Delays

Task scheduling with communication delays is an NP-hard problem. Some previous attempts at finding optimal solutions to this problem have used branch-and-bound state-space search, with promising results. Duplication is an extension to the task scheduling model which allows tasks to be executed multiple times within a schedule, providing benefits to schedule length where this allows a reduction in communication costs. This article proposes the first approach to state-space search for optimal task scheduling with task duplication. Also presented are new definitions for important standard bounding metrics in the context of duplication. An extensive empirical evaluation shows that the use of duplication significantly increases the difficulty of optimal scheduling, but the proposed approach also gives certainty that a large proportion of task graphs can be scheduled more effectively when duplication is allowed, and permits to quantify the exact advantage.