Short survey on graph correlation clustering with minimization criteria

Abstract

In clustering problems one has to partition a given set of objects into some subsets (called clusters) taking into consideration only similarity of the objects. One of the most visual formalizations of clustering is the graph clustering, that is, grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In this short survey, we consider the graph correlation clustering problems where the goal is to minimize the number of edges between clusters and the number of missing edges inside clusters. We present a number of results on graph correlation clustering including results on computational complexity and approximability of different variants of the problems, and performance guarantees of approximation algorithms for graph correlation clustering. Some results on approximability of weighted versions of graph correlation clustering are also presented.