Dynamic diffusion load balancing

We present the first analysis of a simple discrete diffusion scheme for dynamic load balancing. In each round (1-epsilon)n tasks are (arbitrarily) generated over a set of n processors, load is balanced amongst neighbours in some underlying graph, then a single task is deleted from each non-empty processor. We show that the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying "communication" graph be connected, and holds even when epsilon = 0. We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms