: 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. Dioeerent 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. Special heuristics are also presented and are shown to have a better 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 requiremen...

. The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to minimize the makespan, i.e. the maximum task completion time. A simple optimal preemptive policy is proven to stochastically minimize the makespan when the precedence graph belongs to a class of forest-cut graphs. 1. Introduction Parallel programs are usually represented by task graphs which are directed acyclic graphs where vertices represent tasks and arcs represent precedence relations between tasks. The executions of these tasks have to satisfy these precedence constraints in such a way that a task can start execution only when all its predecessor tasks have completed execution. For any given task graph, the scheduling problem consists in assigning tasks to a set of processors in such a wa...