A polynomial algorithm with asymptotic ratio $2/3$ for the asymmetric maximization version of the $m$-PSP

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.