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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 2, Pages 134–143 (Mi timm939)  
This article is cited in 5 scientific papers (total in 6 papers)

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

I. I. Eremina, E. Kh. Gimadib, A. V. Kel'manovb, A. V. Pyatkinb, M. Yu. Khachaiac

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
c Ural Federal University
Full-text PDF (182 kB) Citations (6)
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Abstract: The problem on a minimal 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 special cases. Approximability questions are analyzed. The weak approximability of the problem is established for the general case. A $2$-approximate effective algorithm with time complexity $O(n^2)$ is proposed for cases where vertex weights are nonnegative and edge weights either satisfy the triangle inequality or are squared pairwise distances for some system of points of a Euclidean space.
Keywords: complete undirected graph, clique of fixed size, minimum weight of vertices and edges, subset search, approximability, polynomial approximation algorithm, performance guarantee, time complexity.
Received: 10.02.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 284, Issue 1, Pages 87–95
DOI: https://doi.org/10.1134/S0081543814020084
Bibliographic databases:
Document Type: Article
UDC: 519.16+519.85
Language: Russian
Citation: I. I. Eremin, E. Kh. Gimadi, A. V. Kel'manov, A. V. Pyatkin, M. Yu. Khachai, “$2$-approximate algorithm for finding a clique with minimum weight of vertices and edges”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 134–143; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 87–95
Citation in format AMSBIB
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\paper $2$-approximate algorithm for finding a~clique with minimum weight of vertices and edges
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 2
\pages 134--143
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 284
\issue , suppl. 1
\pages 87--95
\crossref{https://doi.org/10.1134/S0081543814020084}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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