Combinatorics of Point Sets and Arrangements of Objects

点集组合和对象排列

• 批准号: 195353047
• 负责人: Professor Dr. Stefan Felsner
• 金额: --
• 依托单位: Fachgebiet Diskrete Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/195353047?language=en
• 关键词: Combinatorics; Point; Sets; Arrangements; Objects

This CRP focuses on combinatorial properties of discrete sets of points and other simple geometric objects primarily in the plane. In general, geometric graphs are a central topic in discrete and computational geometry, and many important questions in mathematics and computer science can be formulated as problems on geometric graphs. We will, among others, investigate Erdös-Szekeres-type problems, questions on colored point sets, and problems on counting, enumerating and sampling of crossing-free configurations. It is the vision of the members of this CRP to make a massive joint effort in order to gain deeper insight into the structure of long-standing problems in the field, and to contribute major steps towards their final solution.

这个CRP的重点是离散点集和其他简单的几何对象主要在平面上的组合特性。一般来说，几何图是离散和计算几何中的中心主题，数学和计算机科学中的许多重要问题都可以用几何图来表示。我们将，除其他外，调查Erdös-Szekeres型问题，彩色点集的问题，和问题的计数，枚举和采样的交叉自由配置。本区域委员会会议成员的愿景是作出巨大的共同努力，以便更深入地了解该领域长期存在的问题的结构，并为最终解决这些问题采取重大步骤。

项目成果

Non-crossing matchings of points with geometric objects

点与几何对象的非交叉匹配

• DOI: 10.1016/j.comgeo.2012.04.005
• 发表时间: 2013
• 期刊: Comput. Geom.
• 作者: Greg Aloupis;Jean Cardinal;Sébastien Collette;Erik D. Demaine;Martin L. Demaine;Muriel Dulieu;Ruy Fabila Monroy;Vi Hart;Ferran Hurtado;Stefan Langerman;Maria Saumell;Carlos Seara;Perouz Taslakian
• 通讯作者: Perouz Taslakian

Bend-optimal orthogonal graph drawing in the general position model

一般位置模型中的弯曲最优正交图绘制

• DOI: 10.1016/j.comgeo.2013.03.002
• 发表时间: 2014
• 期刊: Comput. Geom.
• 作者: S. Felsner;M. Kaufmann;P. Valtr
• 通讯作者: P. Valtr