We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

翻译：针对最小最大目标的相关性聚类问题，我们提出了可在完全图上实现常数因子近似的快速算法。这些算法是该问题首批纯粹的组合近似算法。我们在顶点集上构造了一种新型半度量（称为相关度量），该度量向聚类算法指示节点对是否应归入同一簇。本文通过实证表明，与先前工作相比，我们的算法在目标质量上牺牲极小，却获得了显著更优的运行时间。此外，我们的算法可扩展至已知算法实质上难以处理的大规模网络。