2-Approximation algorithm for finding a clique with minimum weight of vertices and edges - Eremin, I. I.; Gimadi, E. Kh; Kel’manov, A. V.; Pyatkin, A. V.; Khachai, M. Yu (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.