Pivot based correlation clustering in the presence of good clusters

TL;DR

This paper improves the approximation ratio of pivot-based correlation clustering algorithms by removing good clusters beforehand, demonstrating better performance on synthetic datasets and providing a more accurate clustering approach.

Contribution

It introduces a modified pivot clustering algorithm that enhances approximation ratios by handling good clusters separately, improving upon the classic method.

Findings

Approximation ratio improved to 2.9991

Algorithm performs well on synthetic datasets

Outperforms previous algorithms in identifying good clusters

Abstract

The classic pivot based clustering algorithm of Ailon, Charikar and Chawla [JACM'08] is factor 3, but all concrete examples showing that it is no better than 3 are based on some very good clusters, e.g., a complete graph minus a matching. By removing all good clusters before we make each pivot step, we show that this improves the approximation ratio to $2.9991$. To aid in this, we also show how our proposed algorithm performs on synthetic datasets, where the algorithm performs remarkably well, and shows improvements over both the algorithm for locating good clusters and the classic pivot algorithm.