2-Approximation algorithm for finding a clique with minimum weight of vertices and edges

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 fo...

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Vydané v:Proceedings of the Steklov Institute of Mathematics Ročník 284; číslo Suppl 1; s. 87 - 95
Hlavní autori: Eremin, I. I., Gimadi, E. Kh, Kel’manov, A. V., Pyatkin, A. V., Khachai, M. Yu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.04.2014
Predmet:
Mathematics
Mathematics and Statistics
approximation guarantee
minimum weight of vertices and edges
subset search
time complexity
clique of fixed size
complete undirected graph
polynomial time approximation algorithm
approximability
ISSN:0081-5438, 1531-8605
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Shrnutí: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543814020084