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

Zhixiang Chen (), Bin Fu (), Yong Tang () and Binhai Zhu ()
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Zhixiang Chen: University of Texas—Pan American
Bin Fu: University of New Orleans
Yong Tang: Sun Yat-Sen University
Binhai Zhu: Montana State University

Journal of Combinatorial Optimization, 2006, vol. 11, issue 2, No 7, 203-217

Abstract: Abstract In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane and centers on the grid points, 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 (Asano et al., 2004). We show that if their radii are between two positive constants, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in Fu and Wang (2004), Fu (2006).

Keywords: Width-bounded separator; Disc covering; Approximation algorithms; Randomized algorithms (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-006-7132-y

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