Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering

Vincent Cohen-Addad; Euiwoong Lee; Shi Li; Alantha Newman

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arXiv · 2309.17243

Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering

Vincent Cohen-Addad·Euiwoong Lee·Shi Li·Alantha Newman

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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.

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Vincent Cohen-Addad, Euiwoong Lee, Shi Li, Alantha Newman. 2023-09-29. Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering. https://arxiv.org/abs/2309.17243

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