Maintaining the Extent of a Moving Point Set
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Let S be a set of n moving points in the plane. We give new efficient and compact kinetic data structures for maintaining the diameter, width, and smallest area or perimeter bounding rectangle of S . If the points in S move with algebraic motions, these structures process O(n 2+\eps ) events. We also give constructions showing that Ω(n 2 ) combinatorial changes are possible for these extent functions even if each point is moving with constant velocity. We give a similar construction and upper bound for the convex hull, improving known results.