Connecting a set of circles with minimum sum of radii

Authors:
Erin Wolf Chambers;Sándor P. Fekete;Hella-Franziska Hoffmann;Dimitri Marinakis;Joseph S. B. Mitchell;Venkatesh Srinivasan;Ulrike Stege;Sue Whitesides
Affiliations:
Department of Computer Science, Saint Louis University;Algorithms Group, TU Braunschweig, Braunschweig, Germany;Algorithms Group, TU Braunschweig, Braunschweig, Germany;Kinsol Research Inc., Duncan, BC, Canada and Department of Computer Science, University of Victoria, Victoria, BC, Canada;Department of Applied Mathematics and Statistics, Stony Brook University;Department of Computer Science, University of Victoria, Victoria, BC, Canada;Department of Computer Science, University of Victoria, Victoria, BC, Canada;Department of Computer Science, University of Victoria, Victoria, BC, Canada
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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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.