Fast Combinatorial Algorithms for Min Max Correlation Clustering

TL;DR

This paper presents the first purely combinatorial algorithms for Min Max correlation clustering that achieve constant factor approximations, significantly improving scalability and runtime on large networks.

Contribution

It introduces a novel correlation metric and algorithms that are faster, scalable, and maintain high-quality solutions compared to prior methods.

Findings

Algorithms achieve constant factor approximation.

Significantly faster runtime than previous methods.

Scales to larger networks effectively.

Abstract

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.