Maintenance of geometric extrema ∈
Maintenance of geometric extrema ∈
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几何极值的维护
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
S. Suri
中科院分区：
文献类型：
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作者：
D. Dobkin;S. Suri
令<italic> s </italic>成为一组，<italic> f </italic>：<italic> s </italic>×<italic> s </italic> s </italic>→<italic> r </italic> r <superc> <superccrpt >+</spcrpt>双变量函数和<italic> f </italic>（<italic> x </italic>，<italic> s </italic>）所有元素上的斜体> f </italic>（<italic> x </italic>，<italic> y </italic>） </inline-equation> <Italic> s </italic>。 <italic> x </italic>，<italic> s </italic>）= max {<italic> f </italic>（<italic> x </italic>，<italic>，<italic> s </italic> s </italic> <subscrpt> 1 </subscrpt>），<italic> f </italic>（<italic> x </italic>，<italic> s </italic> </italic> <subscrpt> 2 </subscrpt>），…，<italic> f < /italic>（<Italic> x </italic>，<italic> s <subscrpt> k </subscrpt> </italic>）}对于任何分解<italic> s </italic> s </italic> =μ<subscrpt> <italic> <italic> <italic> i </italic> = 1 </subscrpt> <supscrpt> <italic> i </italic> = <italic> k </italic> </italic> </supscrpt> <italic> s <s <sebcrpt> i </subscrpt> i </sisscrpt> </italic >计算可分解功能的最大值（最小值）是在本文中固有的。并从集合<italic> s </italic>中删除该技术包括用于<italic>动态</Italic>计算直径或最接近一组点的有效算法最小的区域（周长）由一组问题确定。
Let <italic>S</italic> be a set, <italic>f</italic>: <italic>S</italic>×<italic>S</italic>→<italic>R</italic><supscrpt>+</supscrpt> a bivariate function, and <italic>f</italic>(<italic>x</italic>,<italic>S</italic>) the <italic>maximum</italic> value of <italic>f</italic>(<italic>x</italic>,<italic>y</italic>) over all elements <italic>y</italic><inline-equation><f>∈</f></inline-equation><italic>S</italic>. We say that <italic>f</italic> is <italic>decomposable</italic> with respect with the maximum if <italic>f</italic>(<italic>x</italic>,<italic>S</italic>) = max {<italic>f</italic>(<italic>x</italic>,<italic>S</italic><subscrpt>1</subscrpt>),<italic>f</italic>(<italic>x</italic>,<italic>S</italic><subscrpt>2</subscrpt>),…,<italic>f</italic>(<italic>x</italic>,<italic>S<subscrpt>k</subscrpt></italic>)} for any decomposition <italic>S</italic> = μ<subscrpt><italic>i</italic>=1</subscrpt><supscrpt><italic>i</italic>=<italic>k</italic></supscrpt><italic>S<subscrpt>i</subscrpt></italic>. Computing the maximum (minimum) value of a decomposable function is inherent in many problems of computational geometry and robotics. In this paper, a general technique is presented for updating the maximum (minimum) value of a decomposable function as elements are inserted into and deleted from the set <italic>S</italic>. Our result holds for a <italic>semi-online</italic> model of dynamization: When an element is inserted, we are told how long it will stay. Applications of this technique include efficient algorithms for <italic>dynamically</italic> computing the diameter or closest pair of a set of points, minimum separation among a set of rectangles, smallest distance between a set of points and a set of hyperplanes, and largest or smallest area (perimeter) retangles determined by a set of points. These problems are fundamental to application areas such as robotics, VLSI masking, and optimization.