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Completeness of vector discrete optimization problems

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References

  1. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall, Englewood Cliffs NJ (1982).

    Google Scholar 

  2. M. R. Garey and D. S. Johnson, Computers and Intractability, Freeman, San Francisco (1979).

    Google Scholar 

  3. V. S. Mikhalevich, V. A. Trubin, and N. Z. Shor, Optimization Problems in Production-Transportation Planning: Models, Methods, and Algorithms [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  4. V. A. Emelichev and M. K. Kravtsov, “Completeness of multicriterial problems on systems of subsets,” Dokl. Akad. Nauk Belarus,38, No. 3, 25–28 (1994).

    MathSciNet  Google Scholar 

  5. V. A. Emelichev and V. A. Perepelitsa, “Multicriterial problems for spanning subtrees of a graph,” Dokl. Akad. Nauk SSSR,298, No. 3, 544–547 (1988).

    Google Scholar 

  6. V. A. Emelichev and V. A. Perepelitsa, “Complete problems of multicriterial discrete optimization,” Soobshcheniya Akad. Nauk GruzSSR,131, No. 3, 502–504 (1988).

    MathSciNet  Google Scholar 

  7. V. A. Emelichev and V. A. Perepelitsa, “Computational complexity of multicriterial problems,” Izv. Akad. Nauk SSSR, Tekhn. Kibern., No. 1, 78–85 (1988).

    MathSciNet  Google Scholar 

  8. V. A. Perepelitsa, Multicriterial Problems of Graph Theory, An Algorithmic Approach [in Russian], UMK VO, Kiev (1989).

    Google Scholar 

  9. V. A. Emelichev and V. A. Perepeliza, “Complexity of vector optimization problems on graphs,” Optimization22, No. 6, 903–918 (1991).

    MathSciNet  Google Scholar 

  10. I. V. Sergienko, Mathematical Models and Methods for Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  11. E. Girlikh and M. M. Kovalev, “The class of polyhedra of the standardization problem with a maximum number of vertices,” Izv. Akad. Nauk BSSR, Ser. Phys.-Math. Sci., No. 6, 29–34 (1974).

    Google Scholar 

  12. V. A. Emelichev and V. A. Perepelitsa, “Cardinality of the set of alternatives in discrete multicriterial problems,” Diskr. Matem.,3, No. 3, 3–12 (1991).

    Google Scholar 

  13. I. V. Sergienko and V. A. Perepelitsa, “Finding the set of alternatives in discrete multicriterial problems,” Kibernetika, No. 5, 85–93, (1987).

    MathSciNet  Google Scholar 

  14. N. Christofides, Graph Theory: An Algorithmic Approach, Academic Press, New York (1975).

    Google Scholar 

  15. V. A. Emelichev and V. A. Perepelitsa, “Complexity of multicriterial transportation problems,” Dokl. Akad. Nauk BSSR,30, No. 7, 593–596 (1986).

    MathSciNet  Google Scholar 

  16. M. K. Kravtsov “Topics of polyhedral combinatorics in trasportation problems with exclusions,” Kibernetika, No. 6, 63–84 (1990).

    MATH  Google Scholar 

  17. V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs, and Optimization [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  18. A. A. Korbut and Yu. Yu. Finkel'shtein, Discrete Programming [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  19. V. A. Perepelitsa and I. V. Sergienko, “A study of a class of integer multicriterial problems,” Zh. Vychisl. Matem. i Mat. Fiziki,28, No. 3, 400–419 (1988).

    MathSciNet  Google Scholar 

  20. M. K. Kravtsov, “Truncated polyhedra with a maximum number of vertices,” Izv. Akad. Nauk Belarus, Ser. Phys.-Math. Sci., No. 3, 30–33 (1993).

    MATH  Google Scholar 

  21. M. K. Kravtsov and V. A. Emelichev, “Some topics of polyhedral combinatorics in generalized transportation problems,” Ekon. Mat. Metody,24, No. 2, 319–326 (1988).

    MathSciNet  Google Scholar 

  22. M. K. Kravtsov, “Proof of Hirsch's conjecture for a class of transportation polyhedra,” Diskr. Matem.,4, No. 2, 23–31 (1992).

    MATH  Google Scholar 

  23. I. I. Melamed, “Optimization methods in transportation,” INT VINIT, ser. Organization of Transportation Management, Vol. 10 (1991).

  24. P. Hansen, “Bicriterial path problem,” Lect. Notes Econ. Math. Syst., vol. 177, 109–127 (1980).

    MATH  Google Scholar 

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 75–83, September–October, 1994.

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Emelichev, V.A., Kravtsov, M.K. Completeness of vector discrete optimization problems. Cybern Syst Anal 30, 693–699 (1994). https://doi.org/10.1007/BF02367750

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  • DOI: https://doi.org/10.1007/BF02367750

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