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A '''kinetic smallest enclosing disk''' data structure is a [[kinetic data structure]] that maintains the [[Smallest_circle_problem|smallest enclosing disk]] of a set of moving points.
== 2D ==
In 2 dimensions, the best known kinetic smallest enclosing disk data structure uses the farthest point delaunay triangulation of the point set to maintain the smallest enclosing disk <ref name="DEGS10"></ref>. The farthest-point [[Delaunay triangulation]] is the [[Duality_(projective_geometry)|dual]] of the [[Voronoi diagram#Higher-order Voronoi diagrams|farthest-point Voronoi diagram]]. It is known that if the farthest-point delaunay triangulation of a point set contains an acute triangle, the [[circumcircle]] of this triangle is the smallest enclosing disk. Otherwise, the smallest enclosing disk is has the diameter of the point set as it's diameter. Thus, by maintaining the [[kinetic diameter]] of the point set, the farthest-point delaunay triangulation, and whether or not the farthest-point delaunay triangulation has a acute triangle, the smallest enclosing disk can be maintained.
This data structure is responsive and compact, but not local or efficient:<ref name="DEGS10"></ref>
* '''Responsiveness:''' This data structure requires <math>O(\log^2 n)</math> time to process each certificate failure, and thus is responsive.
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