Parallel and Memory-limited Algorithms for Optimal Task Scheduling Using a Duplicate-Free State-Space

Abstract: The problem of task scheduling with communication delays is strongly NP-hard. State-space search algorithms such as A* have been shown to be a promising approach to solving small to medium sized instances optimally. A recently proposed state-space model for task scheduling, known as Allocation-Ordering (AO), allows state-space search methods to be applied without the need for previously necessary duplicate avoidance mechanisms, and resulted in significantly improved A* performance. The property of a duplicate-free state space also holds particular promise for memory limited search algorithms, such as depth-first branch-and-bound (DFBnB), and parallel search algorithms. This paper investigates and proposes such algorithms for the AO model and, for comparison, the older Exhaustive List Scheduling (ELS) state-space model. Our extensive evaluation shows that AO gives a clear advantage to DFBnB and allows greater scalability for parallel search algorithms.