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Computation of lower bounds on the network cost in location problems subject to distance constraints

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Abstract

Methods for the computation of lower bounds on the cost of the connecting network for the continuous and discrete variants of the problem of location of interconnected objects subject to minimal or maximal distances between them are proposed. For the continuous variant, the bound is found by solving a linear programming problem. For the discrete variant, an assignment problem with a rectangular matrix containing forbidden entries is constructed. An application of the assignment problem for locating objects of various sizes is described.

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References

  1. G. G. Zabudsky, “On an Integer-Valued Statement of a Location Problem of Objects on a Line,” in Control Systems (Novosibirsk, 1990), No. 30, pp. 35–45 [in Russian].

  2. R. E. Burcard and K. Stratmamm, “Numerical Investigations on Quadratic Assignment Problems,” Naval. Res. Logist. Quadratic Quart. 25(1), 129–148 (1978).

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  3. V. N. Sachkov, Introduction to Combinatorial Methods in Discrete Mathematics (Nauka, Moscow, 1982) [in Russian].

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  4. M. I. Rubinshtein, “Algorithms for the Assignment Problem,” Avtom. Telemekh., No. 7, 145–154 (1981).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk Branch, Siberian Division, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    G. G. Zabudsky

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  1. G. G. Zabudsky
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Original Russian Text © G.G. Zabudsky, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 2, pp. 216–221.

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Zabudsky, G.G. Computation of lower bounds on the network cost in location problems subject to distance constraints. Comput. Math. and Math. Phys. 46, 206–211 (2006). https://doi.org/10.1134/S0965542506020035

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  • DOI: https://doi.org/10.1134/S0965542506020035

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