A PTAS for a disc covering problem using width-bounded separators

Authors:
Zhixiang Chen;Bin Fu;Yong Tang;Binhai Zhu
Affiliations:
Dept. of Computer Science, University of Texas -Pan American, TX;Dept. of Computer Science, University of New Orleans, LA;Dept. of Computer Science, Sun Yat-Sen University, Guangzhou, China;Dept. of Computer Science, Montana State University, MT
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane, find a subset of discs to maximize the area covered by exactly one disc. This problem originates from the application in digital halftoning, with the best known approximation factor being 5.83 [2]. We show that if the maximum radius is no more than a constant times the minimum radius, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in [5,6].