Computing circular separability

Two sets of planar pointsS1 andS2 are circularly separable if there is a circle that enclosesS1 but excludesS2. 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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