Scheduling at Twilight the Easy Way

We investigate particularly simple algorithms for optimizing the tradeoff between load imbalance and assignment overheads in dynamic multiprocessor scheduling scenarios, when the information that is available about the processing time of a task before it is completed is vague. We describe a simple and elegant generic algorithm that, in a very general model, always comes surprisingly close to the theoretical optimum, and the performance of which we can analyze exactly with respect to constant factors. In contrast, we prove that algorithms that assign tasks in equal-sized portions perform far from optimal in general. In fact, we give evidence that the performance of our generic scheme cannot be improved by any constant factor without sacrificing the simplicity of the algorithm. We also give lower bounds on the performance of the various decreasing-size heuristics that have typically been used so far in concrete applications