Correlation Clustering Beyond the Pivot Algorithm
Abstract
We study the classic correlation clustering in the dynamic setting. Given objects and a complete labeling of the object-pairs as either similar or dissimilar, the goal is to partition the objects into arbitrarily many clusters while minimizing disagreements with the labels. In the dynamic setting, an update consists of a flip of a label of an edge. In a breakthrough result, [BDHSS, FOCS'19] showed how to maintain a 3-approximation with polylogarithmic update time by providing a dynamic implementation of the Pivot algorithm of [ACN, STOC'05]. Since then, it has been a major open problem to determine whether the 3-approximation barrier can be broken in the fully dynamic setting. In this paper, we resolve this problem. Our algorithm, Modified Pivot, locally improves the output of Pivot by moving some vertices to other existing clusters or new singleton clusters. We present an analysis showing that this modification does indeed improve the approximation to below 3. We also show that its output can be maintained in polylogarithmic time per update.
Cite
@article{arxiv.2404.06797,
title = {Correlation Clustering Beyond the Pivot Algorithm},
author = {Soheil Behnezhad and Moses Charikar and Vincent Cohen-Addad and Alma Ghafari and Weiyun Ma},
journal= {arXiv preprint arXiv:2404.06797},
year = {2025}
}