Maximum inscribed and minimum enclosing tropical balls of tropical polytopes and applications to volume estimation and uniform sampling

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-01-27 DOI:10.1016/j.comgeo.2025.102163

David Barnhill , Ruriko Yoshida , Keiji Miura

引用次数: 0

Abstract

We consider a minimum enclosing and maximum inscribed tropical balls for any given tropical polytope over the tropical projective torus in terms of the tropical metric with the max-plus algebra. We show that we can obtain such tropical balls via linear programming. Then we apply minimum enclosing and maximum inscribed tropical balls of any given tropical polytope to estimate the volume of and sample uniformly from the tropical polytope.

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热带多面体的最大内切和最小封闭热带球及其在体积估计和均匀抽样中的应用

我们考虑了在热带射影环面上任意给定热带多面体的最小外接和最大内切的热带球，并给出了具有max-plus代数的热带度量。我们证明了用线性规划可以得到这样的热带球。然后利用任意给定热带多面体的最小外接球和最大内接球来均匀估计热带多面体的体积和样本。

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.