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Dynamic Balanced Graph Partitioning
SIAM Journal on Discrete Mathematics ( IF 0.8 ) Pub Date : 2020-08-12 , DOI: 10.1137/17m1158513
Chen Avin , Marcin Bienkowski , Andreas Loukas , Maciej Pacut , Stefan Schmid

SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1791-1812, January 2020.
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into $L$ clusters, each of size $k$, such that frequently communicating nodes are located in the same cluster. The partitioning can be updated dynamically by migrating nodes between clusters. The goal is to devise online algorithms which jointly minimize the amount of intercluster communication and migration cost. The problem features interesting connections to other well-known online problems. For example, scenarios with $L = 2$ generalize online paging, and scenarios with $k = 2$ constitute a novel online variant of maximum matching. We present several lower bounds and algorithms for settings both with and without cluster-size augmentation. In particular, we prove that any deterministic online algorithm has a competitive ratio of at least $k$, even with significant augmentation. Our main algorithmic contributions are an $O(k \log k)$-competitive deterministic algorithm for the general setting with constant augmentation and a constant competitive algorithm for the maximum matching variant.


中文翻译:

动态平衡图分区

SIAM离散数学杂志,第34卷,第3期,第1791-1812页,2020年1月。
本文从在线角度出发研究经典的平衡图划分问题:给定$ n $节点之间的成对通信请求的任意顺序,其模式可能随时间变化,目的是通过对节点分成$ L $个簇,每个簇的大小为$ k $,这样频繁通信的节点位于同一簇中。可以通过在群集之间迁移节点来动态更新分区。目标是设计在线算法,以共同最小化集群间的通信量和迁移成本。该问题具有与其他知名在线问题的有趣联系。例如,具有$ L = 2 $的方案可以进行在线分页,而具有$ k = 2 $的方案则可以构成新颖的最大匹配在线变量。我们介绍了使用和不使用群集大小增强的设置的几种下界和算法。尤其是,我们证明,即使具有显着增强,任何确定性在线算法都具有至少$ k $的竞争比。我们的主要算法贡献是用于具有恒定扩充的一般设置的$ O(k \ log k)$竞争确定性算法和用于最大匹配变量的恒定竞争算法。
更新日期:2020-08-14
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