Geodesic
Approximate solution of the $p$-median minimization problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1614-1621 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. P. Il'ev; S. D. Il'eva; A. A. Navrotskaya. Approximate solution of the $p$-median minimization problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1614-1621. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a6/

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