Augmenting graphs to minimize the radius

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-08-01 DOI:10.1016/j.comgeo.2023.101996

Joachim Gudmundsson , Yuan Sha

引用次数: 0

Abstract

We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time $(5 / 3 - ϵ)$ -approximation algorithm, for any $ϵ > 0$ , unless $P = N P$ .

We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.

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扩充图形以最小化半径

我们研究了通过增加k条边来扩充度量图的问题，同时最小化扩充图的半径。我们给出了一个简单的3-近似算法，并证明对于任何一个ε>；0，除非P=NP。对于输入图为树的特殊情况，我们还给出了两个精确的算法，其中一个算法被推广到处理具有有界树宽的度量图。

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.