We analyze a tour-uncrossing heuristic for the Travelling Salesperson Problem, showing that its worst-case approximation ratio is $\Omega(n)$ and its average-case approximation ratio is $\Omega(\sqrt{n})$ in expectation. We furthermore evaluate the approximation performance of this heuristic numerically on average-case instances, and find that it performs far better than the average-case lower bound suggests. This indicates a shortcoming in the approach we use for our analysis, which is a rather common approach in the analysis of local search heuristics.

翻译：我们针对旅行商问题中的一种解交叉启发式方法进行了分析，结果表明其最坏情况近似比为$\Omega(n)$，且平均情况下期望近似比为$\Omega(\sqrt{n})$。此外，我们通过数值实验评估了该启发式在平均情况实例上的近似性能，发现其表现远优于平均情况理论下界所预示的结果。这一现象揭示了本文分析方法存在的缺陷——而此类方法正是局部搜索启发式分析中相当常见的途径。