如何在历史中搜索

Q4 Mathematics
Bernard Chazelle
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引用次数: 68

摘要

本文考虑了赋予动态数据结构记忆其以前所处情况的能力的问题。我们提出了一种记录n个对象的有序集S上h个更新历史的新方案,该方案允许在历史中的任何时间进行快速邻居计算。该方法的新颖之处在于,它允许集合S相对于查询仅是部分有序的,并且时间度量是多维的。该方法的通用性使它对三维几何中的许多问题都很有用。例如,我们能够给出快速的算法来定位三维复合体中的一个点,使用线性空间,或者找出n个给定点中最接近查询平面的那个点。使用一种更简单,但概念上相似的技术,我们证明了使用O(n2)预处理,可以在O(log2n)时间内确定E3中n个给定点中哪一个最接近任意查询点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
How to search in history

This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of h updates over an ordered set S of n objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set S to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of n given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with O(n2) preprocessing, it is possible to determine in O(log2 n) time which of n given points in E3 is closest to an arbitrary query point.

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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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