Correlation Clustering via Strong Triadic Closure Labeling: Fast Approximation Algorithms and Practical Lower Bounds

TL;DR

This paper introduces faster, practical approximation algorithms for correlation clustering, especially for cluster editing and deletion, leveraging strong triadic closure principles to improve scalability and solution quality.

Contribution

It presents novel approximation algorithms avoiding complex relaxations, including the first combinatorial approach for cluster deletion, enhancing scalability and practical performance.

Findings

Algorithms scale to much larger problems.

Solutions nearly match the best existing algorithms.

First combinatorial approximation for cluster deletion.

Abstract

Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster approximation algorithms that avoid these relaxations, for two well-studied special cases: cluster editing and cluster deletion. We accomplish this by drawing new connections to edge labeling problems related to the principle of strong triadic closure. This leads to faster and more practical linear programming algorithms, as well as extremely scalable combinatorial techniques, including the first combinatorial approximation algorithm for cluster deletion. In practice, our algorithms produce approximate solutions that nearly match the best algorithms in quality, while scaling to problems that are orders of magnitude larger.