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arXiv · 2006.14093

A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space

Haitao Wang·Yiming Zhao
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Abstract

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.

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Haitao Wang, Yiming Zhao. 2020-06-24. A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space. https://arxiv.org/abs/2006.14093

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