Minimum-width double-slabs and widest empty slabs in high dimensions

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-02-25 DOI:10.1016/j.comgeo.2025.102173

Taehoon Ahn , Chaeyoon Chung , Hee-Kap Ahn , Sang Won Bae , Otfried Cheong , Sang Duk Yoon

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引用次数: 0

Abstract

A slab in d-dimensional space

R^{d}

is the set of points enclosed by two parallel hyperplanes. We consider the problem of finding an optimal pair of parallel slabs, called a double-slab, that covers a given set P of n points in

R^{d}

. We address two optimization problems in

R^{d}

for any fixed dimension

d ⩾ 3

: the minimum-width double-slab problem, in which one wants to minimize the maximum width of the two slabs of the resulting double-slab, and the widest empty slab problem, in which one wants to maximize the gap between the two slabs. Our results include the first nontrivial exact algorithms that solve the former problem for

d ⩾ 3

and the latter problem for

d ⩾ 4

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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.