Existence, uniqueness, and algorithmic computation of general lilypond systems
Existence, uniqueness, and algorithmic computation of general lilypond systems
复制标题
一般睡莲池系统的存在性、唯一性及算法计算
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
G. Last
中科院分区：
文献类型：
--
作者：
Matthias Heveling;G. Last
基于欧几里得空间的局部有限子集φ的lilypond系统定义如下。在时间0，φ的每一点开始以单位速度向各个方向增长，形成一个球系统，其中任何一个特定的球在与另一个球碰撞的瞬间停止增长。基于文[1]中给出的lilypond系统的一个更正式的定义，我们将证明这些系统的存在性和唯一性。我们的方法适用于更一般的设置，其中φ是某些空间的局部有限子集？配备了伪度量d.我们还将推导出一个算法近似的系统，至少线性下降的误差。几个例子将说明我们的一般结果。© 2005 Wiley Periodicals，Inc.随机结构算法，2006
The lilypond system based on a locally finite subset φ of the Euclidean space ℝn is defined as follows. At time 0 every point of φ starts growing with unit speed in all directions to form a system of balls in which any particular ball ceases its growth at the instant that it collides with another ball. Based on a more formal definition of lilypond systems given in 1 , we will prove that these systems exist and are uniquely determined. Our approach applies to the far more general setting, where φ is a locally finite subset of some space ? equipped with a pseudo‐metric d. We will also derive an algorithm approximating the system with at least linearly decreasing error. Several examples will illustrate our general results. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006