Discrete & Computational Geometry最新文献_第10页

Delaunay and Regular Triangulations as Lexicographic Optimal Chains 作为字典最优链的Delaunay和正则三角剖分

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-05-16 DOI: 10.1007/s00454-023-00485-1

D. Cohen-Steiner, A. Lieutier, J. Vuillamy

引用次数: 1

Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two 用平移不变的二阶闵可夫斯基张量重构平面椭圆

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-04-03 DOI: 10.1007/s00454-022-00470-0

Rikke Eriksen, Markus Kiderlen

引用次数: 1

Morphing Triangle Contact Representations of Triangulations 三角形的变形三角形接触表示

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-03-15 DOI: 10.1007/s00454-022-00475-9

Patrizio Angelini, S. Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli

引用次数: 1

Tropical Carathéodory with Matroids. 带拟类的热带油葵。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 DOI: 10.1007/s00454-022-00446-0

Georg Loho, Raman Sanyal

引用次数: 2

Combinatorial Properties and Recognition of Unit Square Visibility Graphs. 单位平方可见性图的组合性质与识别。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2023-03-22 DOI: 10.1007/s00454-022-00414-8

Katrin Casel, Henning Fernau, Alexander Grigoriev, Markus L Schmid, Sue Whitesides

引用次数: 0

Maximum Matchings in Geometric Intersection Graphs. 几何交图中的最大匹配。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2023-09-09 DOI: 10.1007/s00454-023-00564-3

Édouard Bonnet, Sergio Cabello, Wolfgang Mulzer

{"title":"Maximum Matchings in Geometric Intersection Graphs.","authors":"Édouard Bonnet, Sergio Cabello, Wolfgang Mulzer","doi":"10.1007/s00454-023-00564-3","DOIUrl":"10.1007/s00454-023-00564-3","url":null,"abstract":"Let G be an intersection graph of n geometric objects in the plane. We show that a maximum matching in G can be found in <math><mrow><mi>O</mi><mspace></mspace><mo>(</mo><msup><mi>ρ</mi><mrow><mn>3</mn><mi>ω</mi><mo>/</mo><mn>2</mn></mrow></msup><msup><mi>n</mi><mrow><mi>ω</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math> time with high probability, where <math><mi>ρ</mi></math> is the density of the geometric objects and <math><mrow><mi>ω</mi><mo>></mo><mn>2</mn></mrow></math> is a constant such that <math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math> matrices can be multiplied in <math><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mi>ω</mi></msup><mo>)</mo></mrow></math> time. The same result holds for any subgraph of G, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in <math><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mrow><mi>ω</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math> time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in <math><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>Ψ</mi><mo>]</mo></mrow></math> can be found in <math><mrow><mi>O</mi><mspace></mspace><mo>(</mo><msup><mi>Ψ</mi><mn>6</mn></msup><msup><mo>log</mo><mn>11</mn></msup><mspace></mspace><mi>n</mi><mo>+</mo><msup><mi>Ψ</mi><mrow><mn>12</mn><mi>ω</mi></mrow></msup><msup><mi>n</mi><mrow><mi>ω</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math> time with high probability.","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 3","pages":"550-579"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10550895/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41156223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Nearly k-Distance Sets. 近似k距离集。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2023-06-06 DOI: 10.1007/s00454-023-00489-x

Nóra Frankl, Andrey Kupavskii

引用次数: 1

Lonely Points in Simplices. 简约中的孤独点

IF 0.6 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2022-09-29 DOI: 10.1007/s00454-022-00428-2

Maximilian Jaroschek, Manuel Kauers, Laura Kovács

引用次数: 0

Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds. 非算术双曲共轭轨道的尖密度和可通约性。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 DOI: 10.1007/s00454-022-00455-z

Edoardo Dotti, Simon T Drewitz, Ruth Kellerhals

引用次数: 0

Deletion in Abstract Voronoi Diagrams in Expected Linear Time and Related Problems. 期望线性时间中抽象Voronoi图的删除及相关问题。

IF 0.8 3区数学

Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2023-03-25 DOI: 10.1007/s00454-022-00463-z

Kolja Junginger, Evanthia Papadopoulou

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引用次数: 4