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

  • System Analysis and Operations Research
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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 N P-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.

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Authors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    A. V. Panyukov & R. E. Shangin

Authors
  1. A. V. Panyukov
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  2. R. E. Shangin
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Correspondence to A. V. Panyukov.

Additional information

Original Russian Text © A.V. Panyukov, R.E. Shangin, 2016, published in Avtomatika i Telemekhanika, 2016, No. 7, pp. 103–112.

This paper was recommended for publication by P.Yu. Chebotarev, a member of the Editorial Board

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Panyukov, A.V., Shangin, R.E. Algorithm for the discrete Weber’s problem with an accuracy estimate. Autom Remote Control 77, 1208–1215 (2016). https://doi.org/10.1134/S0005117916070079

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