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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kinetic smallest enclosing disk ： ウィキペディア英語版 Kinetic smallest enclosing disk A kinetic smallest enclosing disk data structure is a kinetic data structure that maintains the 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.〔 The farthest-point Delaunay triangulation is the dual of the 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 has the diameter of the point set as its 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 an acute triangle, the smallest enclosing disk can be maintained. This data structure is responsive and compact, but not local or efficient:〔 * Responsiveness: This data structure requires $O(\backslash log^2\; n)$ time to process each certificate failure, and thus is responsive. * Locality: A point can be involved in $\backslash Theta(n)$ certificates. Therefore, this data structure is not local. * Compactness: This data structure requires O(n) certificates total, and thus is compact. * Efficiency: This data structure has $O(n^)$ events total.(for all $\backslash epsilon>0$ The best known lower bound on the number of changes to the smallest enclosing disk is $\backslash Omega(n^2)$. Thus the efficiency of this data structure, the ratio of total events to external events, is $O(n^)$. The existence of kinetic data structure that has $o(n^)$ events is an open problem.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kinetic smallest enclosing disk」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.