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 \(O(mn^3)\).

中文翻译：

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$$ \ boldsymbol m $$ -PSP的非对称最大化版本的渐近比率$$ \ boldsymbol {2/3} $$的多项式算法

摘要

在2005年，Kaplan等人。提出了一种针对非对称TSP最大化版本的具有近似比\（2/3 \）的多项式时间算法。2014年，Glebov，Skretneva和Zambalaeva为非对称\（2 \）- PSP（\（2 \）- APSP-max的最大化版本构造了一种近似算法，近似比率为\（2/3 \）和三次运行时间），需要在一个完整的有向加权图中找到两个最大总权重的边不相交的哈密顿循环。本文的目标是建立一个类似的算法的更一般的\（M \） -APSP-MAX在不对称情况下和证明这个算法倾向于近似比\（2/3 \）作为\（n \）增长，运行时复杂度估计\（O（mn ^ 3）\）。