Labeling Points with Circles

, and . International Journal of Computational Geometry and Applications 11 (2): 181--195 (2001)


We present a new algorithm for labeling points with circles of equal size. Our algorithm tries to maximize the label size. It improves the approximation factor of the only known algorithm for this problem by more than 50 \% to about 1/20. At the same time, our algorithm keeps the $O(n łog n)$ time bound of its predecessor. In addition, we show that the decision problem is NP-hard and that it is NP-hard to approximate the maximum label size beyond a certain constant factor.

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