SIAM Journal on Computing, Ahead of Print.
Among various variants of the traveling salesman problem (TSP), the $s$-$t$-path graph TSP has the special feature that we know the exact integrality ratio, $\frac{3}{2}$, and an approximation algorithm matching this ratio. In this paper, we go below this threshold: we devise a polynomial-time algorithm for the $s$-$t$-path graph TSP with approximation ratio $1.497$. Our algorithm can be viewed as a refinement of the $\frac{3}{2}$-approximation algorithm in [A. Sebö and J. Vygen, Combinatorica, 34 (2014), pp. 597--629], but we introduce several completely new techniques. These include a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which $s$ and $t$ have small distance (which works for general metrics).

中文翻译：

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在图表中以$ s $-$ t $ -Tours击败积分率

《 SIAM计算杂志》，预印本。
在旅行推销员问题（TSP）的各种变体中，$ s $-$ t $-路径图TSP具有我们知道确切的整数比率$ \ frac {3} {2} $和近似值的特殊特征。匹配此比率的算法。在本文中，我们低于此阈值：我们为$ s $-$ t $-路径图TSP设计了多项式时间算法，其近似比为$ 1.497 $。我们的算法可以看作是[A.]中的\\ frac {3} {2} $近似算法的改进。Sebö和J.Vygen，Combinatorica，34（2014），第597--629页]，但我们介绍了几种全新的技术。其中包括一种新型的耳朵分解，增强的入耳感应，揭示了与拟人联合的新颖联系，更强的下界，以及将一般情况简化为$ s $和$ t $距离较小的情况（适用于一般指标）。