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 Diskretn. Anal. Issled. Oper., 2010, Volume 17, Number 3, Pages 19–31 (Mi da609)

On probabilistic analysis of one approximation algorithm for the $p$-median problem

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: An approximation algorithm for solving the $p$-median problem with time complexity $O(n^2)$ and results of its probabilistic analysis are presented. Given an undirected complete graph with distances that are independent random uniformly distributed variables. The objective equals the sum of the random variables. Analysis is based on estimations of the probability of great deviations of those sums. In the paper one of limit theorems for this analysis in the form of Petrov's inequality is used. Moreover, the dependence factor is taken into account. As the results of the probabilistic analysis, the bounds of the relative error, the fault probability and conditions of asymptotic optimality of the algorithm are presented. Ill. 1, bibl. 11.

Keywords: $p$-median problem, approximation algorithm, asymptotic optimality, relative error, fault probability, Petrov's theorem, uniform distribution.

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Bibliographic databases:
UDC: 519.8
Revised: 27.12.2009

Citation: E. Kh. Gimadi, “On probabilistic analysis of one approximation algorithm for the $p$-median problem”, Diskretn. Anal. Issled. Oper., 17:3 (2010), 19–31

Citation in format AMSBIB
\Bibitem{Gim10} \by E.~Kh.~Gimadi \paper On probabilistic analysis of one approximation algorithm for the $p$-median problem \jour Diskretn. Anal. Issled. Oper. \yr 2010 \vol 17 \issue 3 \pages 19--31 \mathnet{http://mi.mathnet.ru/da609} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2732271} \zmath{https://zbmath.org/?q=an:1249.90140} 

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This publication is cited in the following articles:
1. E. Kh. Gimadi, V. T. Dementev, “Veroyatnostnyi analiz detsentralizovannoi versii odnogo obobscheniya zadachi o naznacheniyakh”, Diskretn. analiz i issled. oper., 18:3 (2011), 11–20
2. E. Kh. Gimadi, A. V. Shakhshneyder, “Approximate algorithms with estimates for routing problems on random inputs with a bounded number of customers per route”, Autom. Remote Control, 73:2 (2012), 323–335
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