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arXiv 2302.12201cs.DCcs.DSmath.PR
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任意图上的动态平均负载均衡

Dynamic Averaging Load Balancing on Arbitrary Graphs

Petra Berenbrink, Lukas Hintze, Hamed Hosseinpour, Dominik Kaaser, Malin Rau

摘要:

本文研究一般图上的动态平均负载均衡。我们考虑无限的时间和动态过程,在每一步新的负载项目被分配到随机选择的节点。选择一个匹配,并在该匹配的边缘上平均负载。我们分析了载荷项不可分的离散情形,而且我们的结果也可以推广到载荷项可以任意分割的连续情形。对于匹配的选择,我们考虑三种不同的模型,随机匹配的线性大小,随机匹配只包含单个边缘,和确定性序列的匹配覆盖整个图形。我们限制差异,其定义为最大和最小负载之间的差异。我们的研究结果涵盖了广泛的图形类,据我们所知,我们的分析是离散和动态平均负载均衡过程的第一个结果。作为我们的主要技术贡献,我们开发了一个漂移的结果,使我们能够应用技术的基础上,在一个电气网络的有效电阻的动态负载均衡的设置。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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