Connecting a Set of Circles with Minimum Sum of Radii
Abstract
We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity tree is given. If the connectivity tree is unknown, the problem is NP-hard if there are upper bounds on the radii and open otherwise. We give approximation guarantees for a variety of polynomial-time algorithms, describe upper and lower bounds (which are matching in some of the cases), provide polynomial-time approximation schemes, and conclude with experimental results and open problems.
Keywords
Cite
@article{arxiv.1105.0791,
title = {Connecting a Set of Circles with Minimum Sum of Radii},
author = {Erin Wolf Chambers and Sándor P. Fekete and Hella-Franziska Hoffmann and Dimitri Marinakis and Joseph S. B. Mitchell and Venkatesh Srinivasan and Ulrike Stege and Sue Whitesides},
journal= {arXiv preprint arXiv:1105.0791},
year = {2017}
}
Comments
21 pages, 15 figures, full version of extended abstract that appeared in Proceedings of the 12th Algorithms and Data Structures Symposium (WADS 2011)