Circle Separability Queries in Logarithmic Time

  title={Circle Separability Queries in Logarithmic Time},
  author={Luis Barba and Stefan Langerman and Greg Aloupis},
Let P be a set of n points in the plane. In this paper we study a new variant of the circular separability problem in which a point set P is preprocessed so that one can quickly answer queries of the following form: Given a geometric object Q, report the minimum circle containing P and exluding Q. Our data structure can be constructed in O(n logn) time using O(n) space, and can be used to answer the query when Q is either a circle or a convex m-gon in O(logn) or O(logn+ logm) time, respectively… CONTINUE READING