In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is averaged over the edges of that matching. We analyze the discrete case where load items are indivisible, moreover our results also carry over to the continuous case where load items can be split arbitrarily. For the choice of the matchings we consider three different models, random matchings of linear size, random matchings containing only single edges, and deterministic sequences 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 our knowledge, our analysis is the first result for discrete and dynamic averaging load balancing processes. As our main technical contribution we develop a drift result that allows us to apply techniques based on the effective resistance in an electrical network to the setting of dynamic load balancing.

翻译：本文研究一般图上的动态均值负载均衡问题。我们考虑无限时间动态过程，其中每一步均有新负载项被分配到随机选择的节点上。随后选择一个匹配，并将负载沿该匹配的边进行均值化处理。我们分析负载项不可分割的离散情形，同时我们的结论也适用于负载项可任意分割的连续情形。针对匹配的选择，我们考虑三种模型：线性规模随机匹配、仅含单边的随机匹配，以及覆盖全图的确定性匹配序列。我们界定了差异——即最大负载与最小负载之差。我们的结果覆盖了广泛的图类，并且据我们所知，这是首个针对离散动态均值负载均衡过程的分析。作为主要技术贡献，我们发展了一个漂移结果，使得基于电网络有效电阻的技术可应用于动态负载均衡场景。