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A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space
arXiv - CS - Data Structures and Algorithms Pub Date : 2020-06-24 , DOI: arxiv-2006.14093
Haitao Wang, Yiming Zhao

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of $P$. Previously, the "continuous" version of the problem where a center may be a point in the interior of an edge of the graph was studied and a linear-time algorithm was known. Our "discrete" version of the problem has not been studied before. We present a linear-time algorithm for the problem.

中文翻译:

度量空间中离散半径最优增广路径的线性时间算法

令 $P$ 是嵌入在度量空间中的 $n$ 个顶点的路径图。我们考虑向 $P$ 添加新边的问题,以便最小化结果图的半径,其中任何中心都被约束为 $P$ 的顶点之一。以前,研究了中心可能是图边缘内部的点的问题的“连续”版本,并且已知线性时间算法。我们之前没有研究过这个问题的“离散”版本。我们提出了一个线性时间算法来解决这个问题。
更新日期:2020-06-26
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