A new approximation algorithm for labeling points with circle pairs

Authors:
Minghui Jiang
Affiliations:
Department of Computer Science, Utah State University, Logan, UT
Venue:
Information Processing Letters
Year:
2006

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Abstract

We study the NP-hard problem of labeling points with maximum-radius circle pairs: given n point sites in the plane, find a placement for 2n interior-disjoint uniform circles, such that each site touches two circles and the circle radius is maximized. We present a new approximation algorithm for this problem that runs in O(n log n + n log 1/ε) time and O(n) space and achieves an approximation factor of (2 + √3 + 2√4+ √3)/4 +√3)+ε(≈ 1.486 + ε), which improves the previous best bound of 1.491 + ε.