Discrete and Computational Geometry最新文献

Discrete Morse Theory for Computing Zigzag Persistence 计算之字形持久性的离散莫尔斯理论

Discrete and Computational Geometry Pub Date : 2023-11-15 DOI: 10.1007/s00454-023-00594-x

Clément Maria, Hannah Schreiber

引用次数: 0

Distortion Reversal in Aperiodic Tilings 非周期光栅中的畸变反转

Discrete and Computational Geometry Pub Date : 2023-11-14 DOI: 10.1007/s00454-023-00607-9

Louisa Barnsley, Michael Barnsley, Andrew Vince

引用次数: 0

Spiraling and Folding: The Topological View 螺旋和折叠:拓扑学观点

Discrete and Computational Geometry Pub Date : 2023-11-12 DOI: 10.1007/s00454-023-00603-z

Jan Kynčl, Marcus Schaefer, Eric Sedgwick, Daniel Štefankovič

引用次数: 0

Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries 对称超平面排列特征多项式的计算

Discrete and Computational Geometry Pub Date : 2023-11-07 DOI: 10.1007/s00454-023-00557-2

Taylor Brysiewicz, Holger Eble, Lukas Kühne

引用次数: 1

An $$mathcal {O}(3.82^{k})$$ Time $$textsf {FPT}$$ Algorithm for Convex Flip Distance 凸翻转距离的$$mathcal {O}(3.82^{k})$$ Time $$textsf {FPT}$$算法

Discrete and Computational Geometry Pub Date : 2023-11-05 DOI: 10.1007/s00454-023-00596-9

Haohong Li, Ge Xia

引用次数: 0

On the Structure of Pointsets with Many Collinear Triples 关于具有多个共线三元组的点集的结构

Discrete and Computational Geometry Pub Date : 2023-11-02 DOI: 10.1007/s00454-023-00579-w

József Solymosi

引用次数: 0

Short Topological Decompositions of Non-orientable Surfaces 非定向曲面的短拓扑分解

Discrete and Computational Geometry Pub Date : 2023-11-01 DOI: 10.1007/s00454-023-00580-3

Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay

引用次数: 0

A Topology-Shape-Metrics Framework for Ortho-Radial Graph Drawing 正交径向图绘制的拓扑-形状-度量框架

Discrete and Computational Geometry Pub Date : 2023-11-01 DOI: 10.1007/s00454-023-00593-y

Lukas Barth, Benjamin Niedermann, Ignaz Rutter, Matthias Wolf

{"title":"A Topology-Shape-Metrics Framework for Ortho-Radial Graph Drawing","authors":"Lukas Barth, Benjamin Niedermann, Ignaz Rutter, Matthias Wolf","doi":"10.1007/s00454-023-00593-y","DOIUrl":"https://doi.org/10.1007/s00454-023-00593-y","url":null,"abstract":"Abstract Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the existence of an orthogonal representation that allows to describe such drawings purely combinatorially by only listing the angles between the edges around each vertex and the directions of bends on the edges, but neglecting any kind of geometric information such as vertex coordinates or edge lengths. In this work, we generalize this idea to ortho-radial representations of ortho-radial drawings , which are embeddings into an ortho-radial grid, whose gridlines are concentric circles around the origin and straight-line spokes emanating from the origin but excluding the origin itself. Unlike the orthogonal case, there exist ortho-radial representations that do not admit a corresponding drawing, for example so-called strictly monotone cycles. An ortho-radial representation is called valid if it does not contain a strictly monotone cycle. Our first main result is that an ortho-radial representation admits a corresponding drawing if and only if it is valid. Previously such a characterization was only known for ortho-radial drawings of paths, cycles, and theta graphs (Hasheminezhad et al. in Australas J Combin 44:171–182, 2009), and in the special case of rectangular drawings of cubic graphs (Hasheminezhad et al. in Comput Geom 43(9):767–780, 2010), where the contour of each face is required to be a combinatorial rectangle. Additionally, we give a quadratic-time algorithm that tests for a given ortho-radial representation whether it is valid, and we show how to draw a valid ortho-radial representation in the same running time. Altogether, this reduces the problem of computing a minimum-bend ortho-radial drawing to the task of computing a valid ortho-radial representation with the minimum number of bends, and hence establishes an ortho-radial analogue of the topology-shape-metrics framework for planar orthogonal drawings by Tamassia (SIAM J Comput 16(3):421–444, 1987).","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"40 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

The Limit of $$L_p$$ Voronoi Diagrams as $$prightarrow 0$$ is the Bounding-Box-Area Voronoi Diagram $$L_p$$ Voronoi图的极限为$$prightarrow 0$$是边界框面积Voronoi图

Discrete and Computational Geometry Pub Date : 2023-10-26 DOI: 10.1007/s00454-023-00599-6

Herman Haverkort, Rolf Klein

{"title":"The Limit of $$L_p$$ Voronoi Diagrams as $$prightarrow 0$$ is the Bounding-Box-Area Voronoi Diagram","authors":"Herman Haverkort, Rolf Klein","doi":"10.1007/s00454-023-00599-6","DOIUrl":"https://doi.org/10.1007/s00454-023-00599-6","url":null,"abstract":"Abstract We consider the Voronoi diagram of points in the real plane when the distance between two points a and b is given by $$L_p(a-b)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>-</mml:mo> <mml:mi>b</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> where $$L_p((x,y)) = (|x|^p+|y|^p)^{1/p}.$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>y</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> <mml:msup> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> We prove that the Voronoi diagram has a limit as p converges to zero from above or from below: it is the diagram that corresponds to the distance function $$L_*((x,y)) = |xy|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In this diagram, the bisector of two points in general position consists of a line and two branches of a hyperbola that split the plane into three faces per point. We propose to name $$L_*$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msub> </mml:math> as defined above the geometric $$L_0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> distance .","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"104 7-8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Semialgebraic Range Reporting 关于半代数值域报告

Discrete and Computational Geometry Pub Date : 2023-10-24 DOI: 10.1007/s00454-023-00574-1

Peyman Afshani, Pingan Cheng

引用次数: 0