English

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

Data Structures and Algorithms 2020-06-26 v1 Computational Geometry

Abstract

Let PP be a path graph of nn vertices embedded in a metric space. We consider the problem of adding a new edge to PP so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of PP. 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.

Keywords

Cite

@article{arxiv.2006.14093,
  title  = {A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space},
  author = {Haitao Wang and Yiming Zhao},
  journal= {arXiv preprint arXiv:2006.14093},
  year   = {2020}
}

Comments

A preliminary version to appear in CCCG 2020

R2 v1 2026-06-23T16:36:31.723Z