度量TSP的最小权双树捷径：逼近比的界
Minimum-weight double-tree shortcutting for Metric TSP: Bounding the approximation ratio
摘要：
度量旅行商问题（TSP）是一个经典的NP-难优化问题。度量TSP的双树捷径方法产生了一个指数大小的TSP旅游空间，每个旅游都近似于最多2倍的最优解。我们考虑的问题是在这些旅行中找到一个最接近的近似，即。\emph{minimum-weight double-tree shortcutting}。在此之前，我们给出了一个有效的算法，并进行了实验分析。本文讨论了最小权双树捷径法的最坏逼近比问题。特别地，我们给出了一些特定度量空间中近似比的下界：在离散最短路度量中2的比，在平面欧氏度量中1.622，在平面Minkowski度量中1.666。第一个这些下界是紧的，我们猜想，其他两个边界也紧，特别是最小重量的双树方法提供了一个1.622近似平面欧几里德TSP。
英文摘要：
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e.\ the \emph{minimum-weight double-tree shortcutting}. Previously, we gave an efficient algorithm for this problem, and carried out its experimental analysis. In this paper, we address the related question of the worst-case approximation ratio for the minimum-weight double-tree shortcutting method. In particular, we give lower bounds on the approximation ratio in some specific metric spaces: the ratio of 2 in the discrete shortest path metric, 1.622 in the planar Euclidean metric, and 1.666 in the planar Minkowski metric. The first of these lower bounds is tight; we conjecture that the other two bounds are also tight, and in particular that the minimum-weight double-tree method provides a 1.622-approximation for planar Euclidean TSP.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
