Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [Mach. Learn. '04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimize the number of edges between vertices in different clusters and missing edges between vertices inside the same cluster. This problem has a wide application in data mining and machine learning. We introduce a general framework that transforms existing static correlation clustering algorithms into fully-dynamic ones that work against an adaptive adversary. We show how to apply our framework to known efficient correlation clustering algorithms, starting from the classic 3-approximate Pivot algorithm from Ailon, Charikar and Newman [JACM'08]. Applied to the most recent sublinear $1.485$-approximation algorithm from Cao, Cohen-Addad, Lee, Li, Lolck, Newman, Thorup, Vogl, Yan and Zhang [STOC'25], we get a $1.485$-approximation fully-dynamic algorithm that works with worst-case constant update time. The original static algorithm gets its approximation factor with constant probability, and we get the same against an adaptive adversary in the sense that for any given update step, not known to our algorithm, our solution is a $1.485$-approximation with constant probability when we reach this update. Most of previous dynamic algorithms, including the celebrated result from Behnezhad, Charikar, Ma and Tan [FOCS'19], had approximation factors around $3$ in expectation, and they could only handle an oblivious adversary. A recent algorithm by Braverman, Dharangutte, Pai, Shah, and Wang [AISTATS'25] could handle an adaptive adversary, but it has a large unspecified constant approximation ratio. This contrasts with our general transformation, which works with all the best approximation factors known for the static case.

翻译：相关聚类是一个被广泛研究的问题，最初由Bansal、Blum和Chawla提出（《机器学习》2004年）。其输入是一个无权重、无向图，目标是对顶点进行聚类，以最小化不同簇之间边的数量以及同一簇内缺失边的数量。该问题在数据挖掘和机器学习中具有广泛应用。我们提出一个通用框架，可将现有的静态相关聚类算法转化为能够对抗自适应对手的全动态算法。我们展示了如何将该框架应用于已知的高效相关聚类算法，从Ailon、Charikar和Newman（JACM 2008年）提出的经典3-近似Pivot算法开始。当应用于Cao、Cohen-Addad、Lee、Li、Lolck、Newman、Thorup、Vogl、Yan和Zhang（STOC 2025年）最新提出的次线性1.485-近似算法时，我们得到一个在最坏情况下具有常数更新时间的1.485-近似全动态算法。原始静态算法以常数概率达到其近似因子，而我们在面对自适应对手时达到相同的效果，即对于算法未知的任意给定更新步骤，当我们到达该更新时，我们的解以常数概率是1.485-近似解。先前的大多数动态算法（包括Behnezhad、Charikar、Ma和Tan（FOCS 2019年）的著名成果）的近似因子在期望上约为3，且只能处理不知情对手。Braverman、Dharangutte、Pai、Shah和Wang（AISTATS 2025年）最近提出的算法能处理自适应对手，但其近似比具有较大的未指定常数。这与我们的通用变换形成对比，后者与静态情况下所有最佳已知近似因子兼容。