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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 9, Pages 1614–1621
DOI: https://doi.org/10.7868/S0044466916090088 (Mi zvmmf10457) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Approximate solution of the $p$-median minimization problem

V. P. Il'evab, S. D. Il'evab, A. A. Navrotskayaab

a Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Omsk State University, Omsk, Russia
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DOI: https://doi.org/10.7868/S0044466916090088
Abstract: A version of the facility location problem (the well-known $p$-median minimization problem) and its generalization — the problem of minimizing a supermodular set function — is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the $p$-median minimization problem in terms of the production and transportation cost matrix is obtained.
Key words: combinatorial optimization, $p$-median, supermodular set function, gradient algorithm, performance guarantee.
Funding agency Grant number
Russian Science Foundation 15-11-10009
Received: 16.11.2015
Revised: 16.02.2016
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 9, Pages 1591–1597
DOI: https://doi.org/10.1134/S0965542516090074
Bibliographic databases:
Document Type: Article
UDC: 519.8
Language: Russian
Citation: V. P. Il'ev, S. D. Il'eva, A. A. Navrotskaya, “Approximate solution of the $p$-median minimization problem”, Zh. Vychisl. Mat. Mat. Fiz., 56:9 (2016), 1614–1621; Comput. Math. Math. Phys., 56:9 (2016), 1591–1597
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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