链，科赫链，和点集与许多三角

IF 2.3 2区计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Journal of the ACM Pub Date : 2023-05-23 DOI:https://dl.acm.org/doi/10.1145/3585535

Daniel Rutschmann, Manuel Wettstein

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引用次数: 0

摘要

我们引入了链的抽象概念，它是平面上n个点的序列，由x坐标排序，因此对于三角剖分而言，任意两个连续点之间的边是不可避免的。关于链的结构性质的一般理论被开发出来，同时对它们的三角剖分数量有了一般的理解。我们还描述了一个有趣的新的和具体的结构，我们称之为科赫链，因为它与科赫曲线相似。基于科赫链的特定结构随后显示具有Ω (9.08n)三角剖分。对于平面点集的最大三角剖分数，这是对先前和长期存在的Ω (8.65n)下界的重大改进。

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Chains, Koch Chains, and Point Sets with Many Triangulations

We introduce the abstract notion of a chain, which is a sequence of n points in the plane, ordered by x-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations.

We also describe an intriguing new and concrete configuration, which we call the Koch chain due to its similarities to the Koch curve. A specific construction based on Koch chains is then shown to have Ω (9.08ⁿ) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω (8.65ⁿ) for the maximum number of triangulations of planar point sets.

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来源期刊

Journal of the ACM 工程技术-计算机：理论方法

CiteScore

7.50

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The best indicator of the scope of the journal is provided by the areas covered by its Editorial Board. These areas change from time to time, as the field evolves. The following areas are currently covered by a member of the Editorial Board: Algorithms and Combinatorial Optimization; Algorithms and Data Structures; Algorithms, Combinatorial Optimization, and Games; Artificial Intelligence; Complexity Theory; Computational Biology; Computational Geometry; Computer Graphics and Computer Vision; Computer-Aided Verification; Cryptography and Security; Cyber-Physical, Embedded, and Real-Time Systems; Database Systems and Theory; Distributed Computing; Economics and Computation; Information Theory; Logic and Computation; Logic, Algorithms, and Complexity; Machine Learning and Computational Learning Theory; Networking; Parallel Computing and Architecture; Programming Languages; Quantum Computing; Randomized Algorithms and Probabilistic Analysis of Algorithms; Scientific Computing and High Performance Computing; Software Engineering; Web Algorithms and Data Mining