Worst-Case Analysis of Scheduling Heuristics of Parallel Systems.

It is well-known that most scheduling problems arising from parallel systems are NP-hard, even under very special assumptions. Thus, various suboptimal algorithms, in particular heuristics, were proposed in the literature. Worst-case error bounds are established in this paper for heuristics of makespan minimization of parallel computations. Different parallel computation models are investigated, including interprocessor communication, task duplication, multiprocessor tasks and parallel tasks. Due to the heterogeneity of these systems, scheduling heuristics can be far away from the optimal solutions. These bounds provide insights to the design of scheduling heuristics in order to obtain good performance guarantee than arbitrary heuristics. Moreover, the performance guarantee of these special heuristics is independent of model parameters such as the maximal duplication degree, processor requirement and parallelization degree.