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A Polynomial Algorithm with Asymptotic Ratio \(\boldsymbol {2/3}\) for the Asymmetric Maximization Version of the \(\boldsymbol m \)-PSP

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Abstract

In 2005, Kaplan et al. presented a polynomial-time algorithm with guaranteed approximation ratio \(2/3\) for the maximization version of the asymmetric TSP. In 2014, Glebov, Skretneva, and Zambalaeva constructed a similar algorithm with approximation ratio \(2/3 \) and cubic runtime for the maximization version of the asymmetric \(2 \)-PSP (\(2 \)-APSP-max), where it is required to find two edge-disjoint Hamiltonian cycles of maximum total weight in a complete directed weighted graph. The goal of this paper is to construct a similar algorithm for the more general \(m \)-APSP-max in the asymmetric case and justify an approximation ratio for this algorithm that tends to \(2/3 \) as \(n\) grows and the runtime complexity estimate \(O(mn^3)\).

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Funding

The authors were supported by the Russian Foundation for Basic Research (projects nos. 18–01–00353 and 18–01–00747).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. N. Glebov

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. N. Glebov & S. G. Toktokhoeva

Authors
  1. A. N. Glebov
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  2. S. G. Toktokhoeva
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Correspondence to A. N. Glebov or S. G. Toktokhoeva.

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Translated by Ya.A. Kopylov

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Glebov, A.N., Toktokhoeva, S.G. A Polynomial Algorithm with Asymptotic Ratio \(\boldsymbol {2/3}\) for the Asymmetric Maximization Version of the \(\boldsymbol m \)-PSP. J. Appl. Ind. Math. 14, 456–469 (2020). https://doi.org/10.1134/S1990478920030059

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  • DOI: https://doi.org/10.1134/S1990478920030059

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