The Complexity of Angular Resolution

Q3 Mathematics

Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI:10.7155/jgaa.00634

M. Schaefer

引用次数: 1

Abstract

. The angular resolution of a straight-line drawing of a graph is the smallest angle formed by any two edges incident to a vertex. The angular resolution of a graph is the supremum of the angular resolutions of all straight-line drawings of the graph. We show that testing whether a graph has angular resolution at least π/ (2 k ) is complete for ∃ R , the existential theory of the reals, for every fixed k ≥ 2 . This remains true if the graph is planar and a plane embedding of the graph is fixed.

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角分辨率的复杂性

．直线图的角解析度是由任何两条边与一个顶点相接形成的最小的角。图形的角分辨率是该图形的所有直线图的角分辨率的最大值。我们证明，对于每个固定k≥2的实数存在论∃R，检验图是否具有至少π/ (2k)的角分辨率是完全的。如果图形是平面的，并且图形的平面嵌入是固定的，则此方法仍然成立。

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

Journal of Graph Algorithms and Applications Mathematics-Geometry and Topology

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

50 weeks

期刊介绍： The Journal of Graph Algorithms and Applications (JGAA) is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards and is distributed in electronic form. JGAA is a gold open access journal that charges no author fees. Topics of interest for JGAA include but are not limited to: Design and analysis of graph algorithms: exact and approximation graph algorithms; centralized and distributed graph algorithms; static and dynamic graph algorithms; internal- and external-memory graph algorithms; sequential and parallel graph algorithms; deterministic and randomized graph algorithms. Experiences with graph and network algorithms: animations; experimentations; implementations. Applications of graph and network algorithms: biomedical informatics; computational biology; computational geometry; computer graphics; computer-aided design; computer and interconnection networks; constraint systems; databases; economic networks; graph drawing; graph embedding and layout; knowledge representation; multimedia; social networks; software engineering; telecommunication networks; user interfaces and visualization; VLSI circuits.