Geodesic
Linear convolution of criteria in the vector p-center problem
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 73-82.

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We investigate a linear convolution of criteria and possibility of its application for finding Pareto set in the vector variant of the well-known combinatorial p-center problem. The polynomial algorithm which transforms any vector p-center problem to a solvable problem with the same Pareto set is proposed. An example which illustrates the work of algorithm is performed. 
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Vladimir A. Emelichev; Evgeny E. Gurevsky. Linear convolution of criteria in the vector $p$-center problem. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 73-82. https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a6/

[1] Podinovsky V. V., Nogin V. D., Pareto-optimal solutions of multiobjective problems, Nauka, Moscow, 1982 (in Russian)

[2] Nogin V. D., Decision making in multiobjective medium. Quantitative approach, Fizmatlit, Moscow, 2002 (in Russian) | Zbl

[3] Christofides N., Graph theory. An algorithmic approach, Academic Press, New York–London–San Francisco, 1975 | MR | Zbl

[4] Zambitski D. K., Lozovanu D. D., Algorithms for solving network optimization problems, Shtiintsa, Kishinev, 1983 (in Russian) | MR

[5] Daskin M., Network and discrete location, Wiley, New York, 1995 | MR | Zbl

[6] Emelichev V. A., Perepeliza V. A., “A multiobjective problems on the spanning trees of a graph”, Soviet Math. Dokl., 37:1 (1988), 114–117 | MR | Zbl

[7] Emelichev V. A., Perepeliza V. A., “Complexity of vector optimization problems on graphs”, Optimization, 22:6 (1991), 903–918 | MR | Zbl

[8] Emelichev V. A., Perepeliza V. A., “On insolubility of the vector problems on graphs by the algorithms of linear convolution”, IV Tiraspol symposium of general topology and its applications, Kishinev, 1991, 82–83 (in Russian)

[9] Emelichev V. A., Perepeliza V. A., “Complexity of discrete multicriteria problems”, Discrete Math. Appl., 4:2 (1994), 89–117 | MR | Zbl

[10] Emelichev V. A., Kravtsov M. K., “On the unsolvability of vector discrete optimization problems on systems of subsets in the class of algorithms involving linear convolution of criteria”, Russian Acad. Sci. Dokl. Math., 49:1 (1994), 6–9 | MR | Zbl

[11] Emelichev V. A., Kravtsov M. K., “Problems of discrete vector optimization on systems of subsets which cannot be solved using a linear convolution algorithm”, Comp. Maths. Math. Phys., 34:7 (1994), 933–942 | MR | Zbl

[12] Kravtsov M. K., Yanushkevich O. A., “Solvability of the vector problem by the linear criteria convolution algorithm”, Mathematical notes, 62:4 (1997), 420–425 | DOI | MR | Zbl

[13] Emelichev V. A., Kravtsov M. K., Yanushkevich O. A., “Solvability of a class of discrete vector problems by the algorithm of linear convolution of criteria”, Comp. Maths. Math. Phys., 37:11 (1997), 1362–1365 | MR | Zbl

[14] Girlich E., Kovalev M. M., Kravtsov M. K., Yanushkevich O. A., “Solvability conditions of vector problems using a linear convolution of criteria”, Kibernetika i sistemny analiz, 1999, no. 1, 81–95 (in Russian) | MR

[15] Emelichev V. A., Kravtsov M. K., Yanushkevich O. A., “Solvability of the vector trajectory bottleneck problem using the algorithm of linear convolution of criteria”, Dokl. Belarussian Acad. Sci., 40:4 (1996), 29–33 (in Russian) | MR | Zbl

[16] Khuth D. E., The art of computer programming. Sorting and Searching, Volume 3, Second Edition, Addison-Wesley, Reading, Massachusetts, 1998