A simple factor-3 approximation for labeling points with circles

Authors:
Minghui Jiang;Jianbo Qian;Zhongping Qin;Binhai Zhu;Robert Cimikowski
Affiliations:
Department of Computer Science, Montana State University, Bozeman, MT;Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, Montana State University, Bozeman, MT and Department of Mathematics, Huazhong University of Science and Technology, Wuhan, China;Department of Computer Science, Montana State University, Bozeman, MT;Department of Computer Science, Montana State University, Bozeman, MT
Venue:
Information Processing Letters
Year:
2003

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Abstract

In this paper we present a simple factor-(3 + ε), 0 n logn + n(1/ε)O(1/ε2) log(D3/εD2)) time, for the problem of labeling a set P of n distinct points with uniform circles. (D2 is the closest pair of P and D3 is the minimum diameter of all subsets of P with size three. This problem is known to be NP-hard. Our bound improves the previous factor of 3.6 + ε.