单位圆盘图中L1最短路径的一种优化算法

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-03-01 DOI:10.1016/j.comgeo.2022.101960

Haitao Wang, Yiming Zhao

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引用次数: 2

摘要

平面中点的集合P的单位圆盘图G（P）是以P为其顶点集的图，使得如果P的两个点之间的距离至多为1并且边的权重等于这两个点的距离。给定P和一个源点s∈P，我们考虑了在G（P）中从s到所有其他顶点的最短路径问题。在用L2度量测量距离的L2情况下，该问题已经得到了广泛的研究，并且当前的最佳算法在O（nlog2⁡n）时间，其中n=|P|。在本文中，我们研究了L1的情况，其中距离是在L1度量下测量的（并且每个圆盘变成一个菱形）；我们给出了一个O（nlog⁡n）时间算法，它匹配Ω（nlog⁡n） -时间下限。

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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An optimal algorithm for L1 shortest paths in unit-disk graphs

A unit-disk graph $G (P)$ of a set P of points in the plane is a graph with P as its vertex set such that two points of P are connected by an edge if the distance between the two points is at most 1 and the weight of the edge is equal to the distance of the two points. Given P and a source point $s \in P$ , we consider the problem of finding shortest paths in $G (P)$ from s to all other vertices of $G (P)$ . In the $L_{2}$ case where the distance is measured by the $L_{2}$ metric, the problem has been extensively studied and the current best algorithm runs in $O (n \log^{2} n)$ time, with $n = | P |$ . In this paper, we study the $L_{1}$ case in which the distance is measured under the $L_{1}$ metric (and each disk becomes a diamond); we present an $O (n \log n)$ time algorithm, which matches the $Ω (n \log n)$ -time lower bound.

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.