Geodesic
A polynomial algorithm with~asymptotic ratio~$2/3$ for~the~asymmetric maximization version of~the~$m$-PSP
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 28-52

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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 $O(mn^3)$. Illustr. 2, bibliogr. 29.
Keywords: Hamiltonian cycle, Traveling Salesman Problem, $m$-Peripatetic Salesman Problem, approximation algorithm, guaranteed approximation ratio. 
@article{DA_2020_27_3_a1,
     author = {A. N. Glebov and S. G. Toktokhoeva},
     title = {A polynomial algorithm with~asymptotic ratio~$2/3$ for~the~asymmetric maximization version of~the~$m${-PSP}},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {28--52},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2020_27_3_a1/}
}
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A. N. Glebov; S. G. Toktokhoeva. A polynomial algorithm with~asymptotic ratio~$2/3$ for~the~asymmetric maximization version of~the~$m$-PSP. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 28-52. http://geodesic.mathdoc.fr/item/DA_2020_27_3_a1/