Abstract
Two sets of planar pointsS 1 andS 2 are circularly separable if there is a circle that enclosesS 1 but excludesS 2. We show that deciding whether two sets are circularly separable can be accomplished inO(n) time using linear programming. We also show that a smallest separating circle can be found inO(n) time, and largest separating circles can be found inO(n logn) time. Finally we establish that all these results are optimal.
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O'Rourke, J., Rao Kosaraju, S. & Megiddo, N. Computing circular separability. Discrete Comput Geom 1, 105–113 (1986). https://doi.org/10.1007/BF02187688
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DOI: https://doi.org/10.1007/BF02187688