Elsevier

Computational Geometry

Volume 75, December 2018, Pages 11-21
Computational Geometry

An improved algorithm for diameter-optimally augmenting paths in a metric space

https://doi.org/10.1016/j.comgeo.2018.06.004Get rights and content
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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 such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in O(nlog3n) time. In this paper, based on new observations and different algorithmic techniques, we present an O(nlogn) time algorithm.

Keywords

Diameter
Path graphs
Augmenting paths
Minimizing diameter
Metric space

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A preliminary version of this paper appeared in the Proceedings of the 15th Algorithms and Data Structures Symposium (WADS 2017). This journal version contains all details and proofs that were omitted in the conference version.