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：我们分析了一种针对旅行商问题的路径解缠启发式算法，证明其最坏情况下的近似比为Ω(n)，且期望平均情况下的近似比为Ω(√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，发现其实际表现远优于平均情况的下界。这表明我们分析中所采用的方法存在不足，而该方法在局部搜索启发式的分析中相当常见。