This paper seeks an analytical estimate of the expected distance for visiting an arbitrary subset of independently and uniformly distributed random points within a compact region. This problem has many real-world application contexts such as the emerging on-demand transportation and logistics services (e.g., ridesharing, customized buses). The lower bounds of the expected optimal tour length are analytically derived by considering a so-called “trapping effect”, which explicitly addresses probabilistically the situation that some of the tour legs must connect points that are not neighbors. A parametric approach is developed to estimate the expected optimal tour length for both Euclidean and rectilinear metrics. Numerical experiments demonstrate the validity of these bounds, as well as the closeness of the proposed estimator to simulated results.

中文翻译：

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访问紧凑区域中随机点子集的平均最小距离

本文寻求对访问紧凑区域内独立且均匀分布的随机点的任意子集的预期距离的分析估计。这个问题有许多现实世界的应用场景，例如新兴的按需运输和物流服务（例如，拼车、定制巴士）。预期最佳游览长度的下限是通过考虑所谓的“陷阱效应”来分析得出的，该效应明确地从概率上解决了某些游览线路必须连接非邻居点的情况。开发了一种参数方法来估计欧几里德和直线度量的预期最佳行程长度。数值实验证明了这些界限的有效性，以及所提出的估计量与模拟结果的接近程度。