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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 Well-separated pair decomposition ： ウィキペディア英語版 Well-separated pair decomposition In computational geometry, a well-separated pair decomposition (WSPD) of a set of points $S\; \backslash subset\; \backslash mathbb^d$, is a sequence of pairs of sets $(A\_i,\; B\_i)$, such that each pair is well-separated, and for each two distinct points $p,\; q\; \backslash in\; S$, there exists precisely one pair which separates the two. The graph induced by a well-separated pair decomposition can serve as a k-spanner of the complete Euclidean graph, and is useful in approximating solutions to several problems pertaining to this. == Definition == Let $A,\; B$ be two disjoint sets of points in $\backslash mathbb^d$, $R(X)$ denote the axis-aligned minimum bounding box for the points in $X$, and $s\; >\; 0$ denote the separation factor. We consider $A$ and $B$ to be well-separated, if for each of $R(A)$ and $R(B)$ there exists a d-ball of radius $\backslash rho$ containing it, such that the two spheres have a minimum distance of at least $s\; \backslash rho$. We consider a sequence of well-separated pairs of subsets of $S$, $(A\_1,\; B\_1),\; (A\_2,\; B\_2),\; \backslash ldots,\; (A\_m,B\_m)$ to be a well-separated pair decomposition (WSPD) of $S$ if for any two distinct points $p,\; q\; \backslash in\; S$, there exists precisely one $i$, $1\; \backslash leq\; i\; \backslash leq\; m$, such that either * $p\; \backslash in\; A\_i$ and $q\; \backslash in\; B\_i$, or * $q\; \backslash in\; A\_i$ and $p\; \backslash in\; B\_i$.〔 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「Well-separated pair decomposition」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.