The well known $4/3$ conjecture states that the integrality ratio of the subtour LP is at most $4/3$ for metric Traveling Salesman instances. We present a family of Euclidean Traveling Salesman instances for which we prove that the integrality ratio of the subtour LP converges to $4/3$. These instances (using the rounded Euclidean norm) turn out to be hard to solve exactly with Concorde, the fastest existing exact TSP solver. For a 200 vertex instance from our family of Euclidean Traveling Salesman instances Concorde needs several days of CPU time. This is more than 1,000,000 times the runtime for a TSPLIB instance of similar size. Thus our new family of Euclidean Traveling Salesman instances may serve as new benchmark instances for TSP algorithms.

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欧几里得旅行商问题的难解实例

众所周知的 $4/3$ 猜想指出，对于度量旅行商实例，subtour LP 的完整性比率最多为 $4/3$。我们提出了一系列欧几里得旅行商实例，我们证明了子旅行 LP 的完整性比收敛到 $4/3$。这些实例（使用四舍五入的欧几里得范数）很难用 Concorde（现有最快的精确 TSP 求解器）精确求解。对于来自我们欧几里得旅行商实例家族的 200 个顶点的实例，协和飞机需要几天的 CPU 时间。对于类似大小的 TSPLIB 实例，这是运行时间的 1,000,000 倍以上。因此，我们新的欧几里得旅行商实例系列可以作为 TSP 算法的新基准实例。