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Polynomial algorithms for solving the quadratic assignment problem on networks

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Abstract

Polynomial algorithms for solving the quadratic assignment problem on special types of networks are proposed. The structure of the links between the objects to be located is represented by a graph.

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References

  1. I. S. Akhmedov and I. Kh. Sigal, Arrangement Problem for the Scheme of the State Enterprise Planning and Some Approaches to Its Solution, available from VINITI 1983, Moscow, no. 270 [in Russian].

  2. V. M. Demidenko, “A Generalization of the Strong Solvability Condition for the Quadratic Assignment Problem with anti-Monge and Toeplitz Matrices,” Dokl. National Acad. Sci. Belarusi 47(2), 15–18 (2003).

    MathSciNet  Google Scholar 

  3. G. G. Zabudskii, “Certain Location Problems on Graphs,” Proc. of the XI Baikal Int. Workshop on Optimization Methods and Applications, Irkutsk, 1998, pp. 135–138 [in Russian].

  4. G. G. Zabudskii and A. Yu. Lagzdin, “An Algorithm for the Quadratic Assignment Problem with the Minimax Criterion on a Tree,” in Proc. VII Int. Conf. on the Dynamics of Systems and Mechanisms Omsk, 2009, Vol. 3, pp. 23–27 [in Russian].

  5. N. N. Metel’skii, “Local Optimization Methods in the Bipartite Graph Location Problem,” Zh. Vychisl. Mat. Mat. Fiz. 24(9), 1428–1432 (1984).

    MathSciNet  Google Scholar 

  6. S. I. Sergeev, “The Quadratic Assignment Problem I,” Avtom. Telemekh., No. 8, 127–147 (1999).

  7. R. E. Burkard, E. Çela, G. Rote, and G. J. Woeginger, “The Quadratic Assignment Problem with a Monotone anti-Monge Matrix and a Symmetric Toeplitz Matrix: Easy and Hard Cases,” Math. Program., Ser. B 82, 125–158 (1998).

    Google Scholar 

  8. R. E. Burkard, M. Dell’Amico, and S. Martello, Assignment Problems (SIAM, Philadelphia, 2009).

    MATH  Google Scholar 

  9. E. Çela, The Quadratic Assignment Problem: Theory and Algorithms (Kluwer, Dordrecht, 1998).

    MATH  Google Scholar 

  10. V. M. Demidenko, G. Finke, and V. S. Gordon, “Well Solvable Cases of the Quadratic Assignment Problem with Monotone and Bimonotone Matrices,” J. Math. Modelling Algorithms 5(2), 167–187 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  11. R. Z. Farahani and M. Hekmatfar, Facility Location: Concepts, Models, Algorithms and Case Studies (Physica, Heidelberg, 2009).

    Google Scholar 

  12. G. Finke, R. E. Burkard, and F. Rendl, “Quadratic Assignment Problems,” Ann. Discrete Math., No. 31, 61–82 (1987).

  13. T. C. Koopmans and M. Beckmann, “Assignment Problems and the Location of Economic Activities,” Econometrica 25, 53–76 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  14. G. H. Hardy, J. E. Littlewood, and G. Polya, “The Maximum of a Certain Bilinear Form,” Proc. London Math. Soc. 25, 265–282 (1926).

    Article  Google Scholar 

  15. M. A. Iordanskii, “Graph Location Problems 2,” in Mezhvuz. sb. “Algebraic-Combinatorial Methods in Applied Mathematics” (Gor’ki Gos. Univ., Gorky, 1982), pp. 26–65 [in Russian].

    Google Scholar 

  16. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, San Francisco, 1979; Mir, Moscow, 1982).

    MATH  Google Scholar 

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Correspondence to G. G. Zabudskii.

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Original Russian Text © G.G. Zabudskii, A.Yu. Lagzdin, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 11, pp. 2052–2059.

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Zabudskii, G.G., Lagzdin, A.Y. Polynomial algorithms for solving the quadratic assignment problem on networks. Comput. Math. and Math. Phys. 50, 1948–1955 (2010). https://doi.org/10.1134/S0965542510110175

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