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：我们分析了一种用于旅行商问题的解缠绕启发式算法，证明其最坏情况近似比为$\Omega(n)$，且平均情况近似比期望为$\Omega(\sqrt{n})$。我们进一步通过数值实验评估了该启发式算法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下界所暗示的结果。这表明我们分析方法存在缺陷——而该方法是局部搜索启发式算法分析中相当常用的手段。