A Tight Approximation Algorithm for the Cluster Vertex Deletion Problem

Abstract

We give the first 2-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines the previous approaches, based on the local ratio technique and the management of true twins, with a novel construction of a “good” cost function on the vertices at distance at most 2 from any vertex of the input graph.