Four Algorithms for Correlation Clustering: A Survey

TL;DR

This paper surveys four approximation algorithms for correlation clustering on complete, unweighted graphs, highlighting their approximation ratios and contributions to efficiently partition objects based on pairwise similarity data.

Contribution

It provides a comprehensive overview of four key algorithms for correlation clustering, detailing their approximation guarantees and methodological differences.

Findings

The 2.06-approximation algorithm offers the best theoretical guarantee.

The algorithms vary significantly in approximation ratios, from 2.06 to 17429.

The survey clarifies the strengths and limitations of each approach.

Abstract

In the Correlation Clustering problem, we are given a set of objects with pairwise similarity information. Our aim is to partition these objects into clusters that match this information as closely as possible. More specifically, the pairwise information is given as a weighted graph $G$ with its edges labelled as ``similar" or ``dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of ``disagreements": the sum of the weights of similar edges across clusters and dissimilar edges within clusters. In this exposition we focus on the case when $G$ is complete and unweighted. We explore four approximation algorithms for the Correlation Clustering problem under this assumption. In particular, we describe the following algorithms: (i) the $17429-$approximation algorithm by Bansal, Blum, and Chawla, (ii) the $4-$approximation algorithm by Charikar, Guruswami, and Wirth (iii) the $3-$approximation algorithm by Ailon, Charikar, and Newman (iv) the $2.06-$approximation algorithm by Chawla, Makarychev, Schramm, and Yaroslavtsev.