Correlation Clustering for General Graphs

TL;DR

This paper introduces a new algorithm for correlation clustering on general graphs, providing theoretical insights and approximation guarantees for minimizing disagreements in signed graphs.

Contribution

It presents a novel algorithm for correlation clustering, establishes a necessary and sufficient condition for optimality, and offers a 2-approximation for certain signed graphs.

Findings

Algorithm achieves a 2-approximation for a subclass of signed graphs.

Identifies a condition where the lower bound equals the minimum disagreements.

Provides theoretical bounds and conditions for correlation clustering.

Abstract

Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of disagreements: the number of negative edges inside clusters plus the number of positive edges between clusters. In this paper, we present an algorithm for correlation clustering in general case. Also, we show that there is a necessary and sufficient condition under which the lower bound, maximum number of edge disjoint weakly negative cycles, is equal to minimum number of disagreements. Finally, we prove that the presented algorithm gives a $2$-approximation for a subclass of signed graphs.