Geodesic
A polynomial $3/5$-approximate algorithm for~the~asymmetric maximization version of $3$-PSP
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 2, pp. 30-59

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We present a first polynomial algorithm with guaranteed approximation ratio for the asymmetric maximization version of the asymmetric $3$-Peripatetic Salesman Problem ($3$-APSP). This problem consists in finding the three edge-disjoint Hamiltonian circuits of maximal total weight in a complete weighted digraph. We prove that the algorithm has guaranteed approximation ratio $3/5$ and cubic running-time. Illustr. 18, bibliogr. 27.
Keywords: Hamiltonian cycle, traveling salesman problem, $m$-peripatetic salesman problem, approximation algorithm, guaranteed approximation ratio. 
@article{DA_2019_26_2_a1,
     author = {A. N. Glebov and S. G. Toktokhoeva},
     title = {A polynomial $3/5$-approximate algorithm for~the~asymmetric maximization version of $3${-PSP}},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {30--59},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_2_a1/}
}
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A. N. Glebov; S. G. Toktokhoeva. A polynomial $3/5$-approximate algorithm for~the~asymmetric maximization version of $3$-PSP. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 2, pp. 30-59. http://geodesic.mathdoc.fr/item/DA_2019_26_2_a1/