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An exact algorithm with linear complexity for a problem of visiting megalopolises

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Abstract

A problem of visiting megalopolises with a fixed number of “entrances” and precedence relations defined in a special way is studied. The problem is a natural generalization of the classical traveling salesman problem. For finding an optimal solution, we give a dynamic programming scheme, which is equivalent to a method of finding a shortest path in an appropriate acyclic oriented weighted graph. We justify conditions under which the complexity of the algorithm depends on the number of megalopolises polynomially, in particular, linearly.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    A. G. Chentsov, M. Yu. Khachai & D. M. Khachai

  2. Ural Federal University, Yekaterinburg, 620002, Russia

    A. G. Chentsov, M. Yu. Khachai & D. M. Khachai

Authors
  1. A. G. Chentsov
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  2. M. Yu. Khachai
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  3. D. M. Khachai
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Correspondence to A. G. Chentsov.

Additional information

Original Russian Text © A.G. Chentsov, M.Yu. Khachai, D.M.Khachai, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 3.

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Chentsov, A.G., Khachai, M.Y. & Khachai, D.M. An exact algorithm with linear complexity for a problem of visiting megalopolises. Proc. Steklov Inst. Math. 295 (Suppl 1), 38–46 (2016). https://doi.org/10.1134/S0081543816090054

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  • DOI: https://doi.org/10.1134/S0081543816090054

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