Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering
Abstract
We consider the classic Correlation Clustering problem: Given a complete graph where edges are labelled either or , the goal is to find a partition of the vertices that minimizes the number of the \pedges across parts plus the number of the \medges within parts. Recently, Cohen-Addad, Lee and Newman [CLN22] presented a 1.994-approximation algorithm for the problem using the Sherali-Adams hierarchy, hence breaking through the integrality gap of 2 for the classic linear program and improving upon the 2.06-approximation of Chawla, Makarychev, Schramm and Yaroslavtsev [CMSY15]. We significantly improve the state-of-the-art by providing a 1.73-approximation for the problem. Our approach introduces a preclustering of Correlation Clustering instances that allows us to essentially ignore the error arising from the {\em correlated rounding} used by [CLN22]. This additional power simplifies the previous algorithm and analysis. More importantly, it enables a new {\em set-based rounding} that complements the previous roundings. A combination of these two rounding algorithms yields the improved bound.
Cite
@article{arxiv.2309.17243,
title = {Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering},
author = {Vincent Cohen-Addad and Euiwoong Lee and Shi Li and Alantha Newman},
journal= {arXiv preprint arXiv:2309.17243},
year = {2023}
}