Static to Dynamic Correlation Clustering

Abstract: Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [BBC04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimizing 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 [ACN08]. Applied to the most recent near-linear $1.437$-approximation algorithm from [CCL+25], we get a $1.437$-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 $1.437$-approximation with constant probability when we reach this update. Previous dynamic algorithms had approximation factors around $3$ in expectation, and they could only handle an oblivious adversary.