平面环面最佳分割成较小直径的部分

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2025-05-22 DOI:10.1016/j.disopt.2025.100890

D.S. Protasov , A.D. Tolmachev , V.A. Voronov

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引用次数: 0

摘要

为了使零件的最大直径最小，我们考虑将二维平面环面T2划分为m个集的问题。对于m≤25，我们给出了分区存在的最大直径dm（T2）的数值估计。提出了几种方法来获得这种估计。特别是，我们使用了通过SAT求解器搜索网格分区，多边形分区的全局优化方法，以及周期性六边形平铺的优化方法。对于m=3，利用初等拓扑推理证明了精确估计。

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Optimal partitions of the flat torus into parts of smaller diameter

We consider the problem of partitioning a two-dimensional flat torus

T^{2}

into

m

sets in order to minimize the maximum diameter of a part. For

m ⩽ 25

we give numerical estimates for the maximum diameter

d_{m} (T^{2})

at which the partition exists. Several approaches are proposed to obtain such estimates. In particular, we use the search for mesh partitions via the SAT solver, the global optimization approach for polygonal partitions, and the optimization of periodic hexagonal tilings. For

m = 3

, the exact estimate is proved using elementary topological reasoning.

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.