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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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics Vol. 284; no. Suppl 1; pp. 87 - 95
Main Authors: Eremin, I. I., Gimadi, E. Kh, Kel’manov, A. V., Pyatkin, A. V., Khachai, M. Yu
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2014
Subjects:
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
Online Access:Get full text
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Summary: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