We provide a new simpler approach to the on-line load balancing problem in the case of restricted assignment of temporary weighted tasks. The approach is very general and allows us to derive on-line distributed algorithms whose competitive ratio is characterized by some combinatorial properties of the underlying graph representing the problem. The effectiveness of our approach is shown by the hierarchical server model introduced by Bar-Noy et al. (2001). In this case, our method yields simpler and distributed algorithms whose competitive ratio is at least as good as� the existing ones. Moreover, the
resulting algorithms and their analysis turn out to be simpler. Finally, in all cases the algorithms are optimal up to a constant factor. Some of our results are obtained via a combinatorial characterization of those graphs for which our technique yields O(sqrt(n))-competitive algorithms. Joint work with Giorgio Gambosi, Gaia Nicosia, Paolo Penna, and Walter Unger.