We study a generalization of the well-known traveling salesman problem in a metric space, in which each city is associated with a release time. The salesman has to visit each city at or after its release time. There exists a naive 5/2-approximation algorithm where the salesman simply starts to route the network after all cities are released. Interestingly, this bound has never been improved for more than two decades. In this paper, we revisit the problem and achieve the following results. First, we devise an approximation algorithm with performance ratio less than 5/2 when the number of distinct release times is fixed. Then, we analyze a natural class of algorithms and show that no performance ratio better than 5/2 is possible unless the Metric TSP can be approximated with a ratio strictly less than 3/2, which is a well-known longstanding open question. Finally, we consider a special case where the graph has a heavy edge and present an approximation algorithm with performance ratio less than 5/2.

我们研究了公制空间中众所周知的旅行推销员问题的一般化，其中每个城市都与发布时间相关联。推销员必须在发布时间或之后访问每个城市。存在一种幼稚的5/2近似算法，在该算法中，所有城市发布后，推销员便开始对网络进行路由。有趣的是，这个界限已经超过二十年了。在本文中，我们重新审视了该问题并取得了以下结果。首先，当固定不同释放时间的数量时，我们设计一种性能比小于5/2的近似算法。然后，我们分析了自然的算法类别，结果表明，除非可以严格按照小于3/2的比率近似来衡量Metric TSP，否则不可能有优于5/2的性能比率，这是一个众所周知的长期未解决的问题。最后，我们考虑一种特殊情况，即图的边缘较重，并提出一种性能比小于5/2的近似算法。