The field of a priori optimization is an interesting subfield of stochastic combinatorial optimization that is well suited for routing problems. In this setting, there is a probability distribution over active sets, vertices that have to be visited. For a fixed tour, the solution on an active set is obtained by restricting the solution on the active set. In the well-studied a priori traveling salesman problem, the goal is to find a tour that minimizes the expected length. In the a priori traveling repairman problem (TRP), the goal is to find a tour that minimizes the expected sum of latencies. In this paper, we study the uniform model, where a vertex is in the active set with probability p independently of the other vertices, and give the first constant-factor approximation for a priori TRP.

中文翻译：

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先验的旅行修理工问题

先验优化领域是随机组合优化的一个有趣的子领域，非常适合解决路由问题。在此设置中，活动集（必须访问的顶点）上存在概率分布。对于固定游览，通过限制活动集上的解来获得活动集上的解。在经过充分研究的先验旅行商问题中，目标是找到使预期长度最小的旅行。在先验旅行修理工问题 (TRP) 中，目标是找到最小化预期延迟总和的旅行。在本文中，我们研究了统一模型，其中一个顶点以独立于其他顶点的概率 p 位于活动集中，并给出了先验 TRP 的第一个常数因子近似。