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Multiindex resource distributions for hierarchical systems

  • Control in Social Economic Systems
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Abstract

Resource distribution in hierarchical systems is formulated as a multiindex linear programming problem under transport-type constraints. Conditions under which this problem is reduced to the determination of the minimal-cost circulation in a transport network are stated.

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References

  1. Voronin, A.A. and Mishin, S.P., Optimal’nye ierarkhicheskie struktury (Optimal Hierarchical Structures), Moscow: Inst. Probl. Upravlen., 2003.

    Google Scholar 

  2. Elsasser, R., Monien, B., and Preis, R., Diffusion Schemes for Load Balancing on Heterogeneous Networks, Theory Comput. Syst., 2002, vol. 35, no. 3, pp. 305–320.

    Article  MathSciNet  Google Scholar 

  3. Gairing, M., Lucking, T., Mavronicolas, M., and Monien, B., Computing Nash Equilibria for Scheduling on Restricted Parallel Links, Proc. 36th Annual ACM Sympos. Theory Comput., 2004, pp. 613–622.

  4. Dunne, P.E., Extremal Behavior in Multiagent Contract Negotiation, J. Artificial Intelligence Res., 2005, vol. 23, no. 1, pp. 41–78.

    MATH  MathSciNet  Google Scholar 

  5. Prilutskii, M.Kh., Distribution of a Homogeneous Resource in Tree-Structured Hierarchical Systems, Tr. III Int. Conf. Identification of Systems and Control Problems (SICPRO’2000), Moscow: Inst. Probl. Upravlen., 2000, pp. 2038–2049.

    Google Scholar 

  6. Prilutskii, M.Kh. and Kartomin, A.G., Flow Algorithms for Resource Distribution in Hierarchical Systems, “Issledovano v Rossii,” 2003, no. 39, pp. 444–452 (http://zhurnal.ape.relarn.ru/articles/2003/039.pdf).

  7. Prilutskii, M.Kh., Many-Criteria Distribution of a Homogeneous Resource in Hierarchical Systems, Avtom. Telemekh., 1996, no. 2, pp. 24–29.

  8. Raskin, L.T. and Kirichenko, I.O., Mnogoindeksnye zadachi lineinogo programmirovaniya (Multiindex Linear Programming Problems), Moscow: Radio i Svyaz’, 1982.

    Google Scholar 

  9. Ford, L.R., Jr. and Fulkerson, D.R., Flows in Networks, Princeton: Princeton Univ. Press, 1962. Translated under the title Potoki v setyakh, Moscow: Mir, 1966.

    Google Scholar 

  10. Litvak, B.G. and Rappoport, A.M., Linear Programming Problems admitting a Network Formulation, Ekonom. Mat. Metody, 1970, vol. 6, no. 4, pp. 594–604.

    MathSciNet  Google Scholar 

  11. Papadimitrou, Ch. and Steiglitz, K., Combinatorial Optimization: Algorithms and Complexity, Englewood Cliffs: Prentice Hall, 1982. Translated under the title Kombinatornaya optimizatsiya: Algoritmy i slozhnost’, Moscow: Mir, 1985.

    Google Scholar 

  12. Hu, T.C., Integer Programming and Network Flows, Reading: Addison-Wesley, 1969. Translated under the title Tselochislennoe programmirovanie i potoki v setyakh, Moscow: Mir, 1974.

    Google Scholar 

  13. Manuscript at http://www.microsoft.com/.

  14. Manuscript at http://www.preactor.com/.

  15. Manuscript at http://www.quintiq.com/.

  16. Cherkassky, B.V. and Goldberg, A.V., Negative-Cycle Detection Algorithms, Proc. 4th Eur. Sympos. Algorithms, 1996, pp. 349–363.

  17. Gofman, A.G. and Kraskal, G.B., Integer Boundary Points of Convex Polyhedrons, in Lineinye neravenstva i smezhnye voprosy (Linear Inequalities and Related Problems), Moscow: Inostrannaya Literatura, 1959.

    Google Scholar 

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Original Russian Text © L.G. Afraimovich, M.Kh. Pributskii, 2006, published in Avtomatika i Telemekhanika, 2006, No. 6, pp. 194–205.

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

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Afraimovich, L.G., Prilutskii, M.K. Multiindex resource distributions for hierarchical systems. Autom Remote Control 67, 1007–1016 (2006). https://doi.org/10.1134/S0005117906060130

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