A better algorithm for an ancient scheduling problem

We consider the online multiprocessor scheduling problem first considered by Graham in 1966 which can be formulated as the following online load-balancing problem: a set of jobs arrive on-line, and each job must be immediately and irrevocably assigned to one ofmidentical machines without any knowledge of future jobs. The goal of the load balancer is to minimize the maximum load on any machine. We present the algorithm CHASM?that outperforms all previously published algorithms for anym?8 and has a competitive ratio of at most 1.945 for allm(the best known lower bound is 1.837). We show that our analysis of CHASM?is almost tight by presenting a lower bound of 1.9378 on its competitive ratio for largem. We also explore some of the trade-offs between any algorithm's worst case and average case performance, and we consider the case when jobs have finite, unknown duration.