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In this paper we study dynamic averaging load balancing on general graphs. Weconsider infinite time and dynamic processes, where in every step new loaditems are assigned to randomly chosen nodes. A matching is chosen, and the loadis averaged over the edges of that matching. We analyze the discrete case whereload items are indivisible, moreover our results also carry over to thecontinuous case where load items can be split arbitrarily. For the choice ofthe matchings we consider three different models, random matchings of linearsize, random matchings containing only single edges, and deterministicsequences of matchings covering the whole graph. We bound the discrepancy,which is defined as the difference between the maximum and the minimum load.Our results cover a broad range of graph classes and, to the best of ourknowledge, our analysis is the first result for discrete and dynamic averagingload balancing processes. As our main technical contribution we develop a driftresult that allows us to apply techniques based on the effective resistance inan electrical network to the setting of dynamic load balancing.

Dynamic Averaging Load Balancing on Arbitrary Graphs