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

In this paper we present a fast and accurate procedure called clustered low rank matrix approximation for massive graphs. The procedure involves a fast clustering of the graph and then approximates each cluster separately using existing methods, e.g. the singular value decomposition, or stochastic algorithms. The cluster-wise approximations are then extended to approximate the entire graph. Thi...