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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 2, Pages 134–143 (Mi timm939)  

This article is cited in 3 scientific papers (total in 4 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

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.

Full text: PDF file (182 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 284, suppl. 1, 87–95

Bibliographic databases:

UDC: 519.16+519.85
Received: 10.02.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Berdyshev, V. V. Vasin, S. V. Matveev, A. A. Makhnev, Yu. N. Subbotin, N. N. Subbotina, V. N. Ushakov, M. Yu. Khachai, A. G. Chentsov, “Ivan Ivanovich Eremin”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 1–8  mathnet  crossref  mathscinet  isi  elib
    2. E. Kh. Gimadi, A. V. Kel'manov, A. V. Pyatkin, M. Yu. Khachai, “Efficient algorithms with performance estimates for some problems of finding several cliques in a complete undirected weighted graph”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 88–101  mathnet  crossref  mathscinet  isi  elib
    3. A. V. Kel'manov, V. I. Khandeev, “A randomized algorithm for two-cluster partition of a set of vectors”, Comput. Math. Math. Phys., 55:2 (2015), 330–339  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. V. Kel'manov, V. I. Khandeev, “An exact pseudopolynomial algorithm for a bi-partitioning problem”, J. Appl. Industr. Math., 9:4 (2015), 497–502  mathnet  crossref  crossref  mathscinet  elib
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