Algorithms for radius-optimally augmenting trees in a metric space

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-10-01 DOI:10.1016/j.comgeo.2023.102018

Joachim Gudmundsson , Yuan Sha

引用次数: 0

Abstract

Let T be a tree with n vertices in a metric space. We consider the problem of adding one shortcut edge to T to minimize the radius of the resulting graph.

For the continuous version of the problem where a center may be a point in the interior of an edge of the graph we give a linear time algorithm. In the case when the center is restricted to lie on a vertex, the discrete version, we give an $O (n \log n)$ expected time algorithm.

Previously linear-time algorithms were known for the special case when the input graph is a path.

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度量空间中半径最优扩充树的算法

设T是一个在度量空间中有n个顶点的树。我们考虑向T添加一条快捷边以最小化生成图的半径的问题。对于问题的连续版本，其中中心可能是图边缘内部的一个点，我们给出了一个线性时间算法。在中心被限制在一个顶点上的情况下，离散形式，我们给出了一个O（nlog⁡n）预期时间算法。以前的线性时间算法对于输入图是路径的特殊情况是已知的。

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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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.