A Duplicate-Free State-Space Model for Optimal Task Scheduling

Abstract

The problem of task scheduling with communication delays (P|prec,cij|Cmax ) is NP-hard, and therefore solutions are often found using a heuristic method. However, an optimal schedule can be very useful in applications such as time critical systems, or as a baseline for the evaluation of heuristics. Branch-and-bound algorithms such as A* have previously been shown to be a promising approach to the optimal solving of this problem, using a state-space model which we refer to as exhaustive list scheduling. However, this model suffers from the possibility of producing high numbers of duplicate states. In this paper we define a new state-space model in which we divide the problem into two distinct subproblems: first we decide the allocations of all tasks to processors, and then we order the tasks on their allocated processors to produce a complete schedule. This two-phase state-space model offers no potential for the production of duplicates. An empirical evaluation shows that the use of this new state-space model leads to a marked reduction in the number of states considered by an A* search in many cases, particularly for task graphs with a high communication-to-computation ratio. With additional refinement, and the development of specialised pruning techniques, the performance of this state-space model could be improved.