定位服务设施和快速公交线路
Locating a service facility and a rapid transit line
摘要：
在本文中，我们研究了一个平面上的设施选址问题，其中一个单一的点（设施）和快速交通线（公路）同时定位，以最小化的总旅行时间的客户端的设施，使用$L_1$或曼哈顿度量。快速公交线路用一条定长、任意方向的线段表示。高速公路是一种替代交通系统，可供客户使用，以减少他们到设施的旅行时间。这个问题是由Espejo和Chía在[7]中提出的。他们给出了最优解的特征和在$O(n^3\log n)$时间内运行的算法，其中$n$表示客户端的数量。在本文中，我们表明，Espejo和Chía的算法并不总是正确的工作。同时，我们给出了解的一个较简单的证明，并给出了一个在$O(n^3)$时间内求解该问题的算法。
英文摘要：
In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the $L_1$ or Manhattan metric. The rapid transit line is represented by a line segment with fixed length and arbitrary orientation. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. This problem was introduced by Espejo and Chía in [7]. They gave both a characterization of the optimal solutions and an algorithm running in $O(n^3\log n)$ time, where $n$ represents the number of clients. In this paper we show that the Espejo and Chía's algorithm does not always work correctly. At the same time, we provide a proper characterization of the solutions with a simpler proof and give an algorithm solving the problem in $O(n^3)$ time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
