线性约束框架的全局刚性

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-02-06 DOI:10.1137/22m151707x

James Cruickshank, Fatemeh Mohammadi, Harshit J. Motwani, Anthony Nixon, Shin-ichi Tanigawa

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 743-763 页，2024 年 3 月。摘要。我们在[math]中考虑了条形连接框架的全局刚度问题，其中每个顶点都被约束在特定的直线上。在我们的设置中，我们允许多个顶点被约束在同一条直线上。在这种情况下，我们给出了任意线集一般刚性的组合特征。此外，在给定线集的温和假设下，我们给出了一般全局刚性图的完整组合特征。这给出了著名的二维全局刚性组合特征的[数学]维扩展。特别是，我们的结果意味着全局刚性是这种情况下的一个通用属性。

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Global Rigidity of Line Constrained Frameworks

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 743-763, March 2024.
Abstract. We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in [math]. In our setting, we allow multiple vertices to be constrained to the same line. We give a combinatorial characterization of generic rigidity in this setting for arbitrary line sets. Further, under a mild assumption on the given set of lines, we give a complete combinatorial characterization of graphs that are generically globally rigid. This gives a [math]-dimensional extension of the well-known combinatorial characterization of two-dimensional global rigidity. In particular, our results imply that global rigidity is a generic property in this setting.

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.