{"title":"The Complexity of Angular Resolution","authors":"M. Schaefer","doi":"10.7155/jgaa.00634","DOIUrl":null,"url":null,"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.","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"1 1","pages":"565-580"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Algorithms and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7155/jgaa.00634","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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.
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.
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