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

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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. Eremin^a, E. Kh. Gimadi^b, A. V. Kel'manov^b, A. V. Pyatkin^b, M. Yu. Khachai^ac

^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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Linking options:

https://www.mathnet.ru/eng/timm939

https://www.mathnet.ru/eng/timm/v19/i2/p134

This publication is cited in the following 6 articles:

Gennady G. Zabudsky, Natalia S. Veremchuk, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 131
Bianca Camille Silmaro, Geoffrey A. Solano, 2019 10th International Conference on Information, Intelligence, Systems and Applications (IISA), 2019, 1
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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