2-Approximation algorithm for finding a clique with minimum weight of vertices and edges
Ivan I. Eremin, Edward Kh. Gimadi, Alexander V. Kel’manov, A. V. Pyatkin, Michael Khachay · Proceedings of the Steklov Institute of Mathematics · 2014
The problem of finding a minimum clique (with respect to the total weight of its vertices and edges) of fixed size in a complete undirected weighted graph is considered along with some of its important subclasses. Approximability issues are analyzed. The inapproximability of the problem is proved for the general case. A 2-approximation efficient algorithm with time complexity O(n 2) is suggested for the cases when vertex weights are nonnegative and edge weights either satisfy the triangle inequality or are squared pairwise distances for some point configuration of Euclidean space.