Algorithms of optimal covering of 2D sets with dynamical metrics

IF 0.3 Q4 MATHEMATICS
P. Lebedev, A. Lempert, A. Kazakov
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引用次数: 0

Abstract

The paper deals with the problem of constructing the thinnest covering for a convex set by a set of similar elements. As a distance between two points, we use the shortest time it takes to achieve one point from another, and the boundary of each covering circle is an isochron. Such problems arise in applications, particularly in sonar and underwater surveillance systems. To solve the problems of covering with such circles and balls, we previously proposed algorithms based both on variational principles and geometric methods. The purpose of this article is to construct coverings when the characteristics of the medium change over time. We propose a computational algorithm based on the theory of wave fronts and prove the statement about its properties. Illustrative calculations are performed.
二维动态度量集的最优覆盖算法
本文研究了用一组相似元素构造凸集的最薄覆盖问题。作为两点之间的距离,我们使用从一个点到达另一个点所需的最短时间,并且每个覆盖圆的边界是一条等时线。这些问题在应用中出现,特别是在声纳和水下监视系统中。为了解决这些圆和球的覆盖问题,我们之前提出了基于变分原理和几何方法的算法。本文的目的是在介质的特性随时间变化时构建覆盖物。我们提出了一种基于波前理论的计算算法,并证明了它的性质。进行了说明性计算。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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