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 Avtomat. i Telemekh.: Year: Volume: Issue: Page: Find

 Avtomat. i Telemekh., 2016, Issue 7, Pages 103–112 (Mi at14509)

System Analysis and Operations Research

Algorithm for the discrete Weber's problem with an accuracy estimate

A. V. Panyukov, R. E. Shangin

South Ural State University, Chelyabinsk, Russia

Abstract: We consider a relaxation of the quadratic assignment problem without the constraint on the number of objects assigned to a specific position. This problem is $NP$-hard in the general case. To solve the problem, we propose a polynomial algorithm with guaranteed posterior accuracy estimate; we distinguish a class of problems with special assignment cost functions where the algorithm is $2$-approximate. We show that if the graph in question contains one simple loop, and the set of assignment positions is a metric space, the proposed algorithm is $2$-approximate and guaranteed to be asymptotically exact. We conduct a computational experiment in order to analyze the algorithm's errors and evaluate its accuracy.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Â37.21.0395 This work was supported by the Ministry of Education and Science of the Russian Federation, contract no. 14.B37.21.0395.

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English version:
Automation and Remote Control, 2016, 77:7, 1208–1215

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Presented by the member of Editorial Board: Ï. Þ. ×åáîòàðåâ

Citation: A. V. Panyukov, R. E. Shangin, “Algorithm for the discrete Weber's problem with an accuracy estimate”, Avtomat. i Telemekh., 2016, no. 7, 103–112; Autom. Remote Control, 77:7 (2016), 1208–1215

Citation in format AMSBIB
\Bibitem{PanSha16} \by A.~V.~Panyukov, R.~E.~Shangin \paper Algorithm for the discrete Weber's problem with an accuracy estimate \jour Avtomat. i Telemekh. \yr 2016 \issue 7 \pages 103--112 \mathnet{http://mi.mathnet.ru/at14509} \elib{http://elibrary.ru/item.asp?id=27182807} \transl \jour Autom. Remote Control \yr 2016 \vol 77 \issue 7 \pages 1208--1215 \crossref{https://doi.org/10.1134/S0005117916070079} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000379745700007} \elib{http://elibrary.ru/item.asp?id=27018447} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84978204021}