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

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 fi nd 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 ) . DOI