EAGER: Geometry and Combinatorics of Intersections and Contacts

EAGER：交叉点和接触点的几何和组合学

• 批准号: 1624382
• 负责人: Stephen Kobourov
• 金额: $ 6万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-15 至 2018-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1624382&HistoricalAwards=false
• 关键词: EAGER; Geometry; Combinatorics; Intersections; Contacts

Put coins flat on a table and push them together. Recording the pairs of coins gives a "contact graph." The simple abstraction of a "graph" as recording connections between objects is surprisingly powerful: computers on the internet, tournament brackets, social networks, and PERT charts are all usefully viewed as graphs. Graphs that have geometric realizations as contacting or intersecting objects in two or more dimensions have special properties (e.g. it has been known for 80 or 40 years that graphs that can be drawn with no crossings can be realized as contact graphs of coins.) This project considers what types of graphs can be contact graphs or intersections graphs of various geometric objects in 2, 3 or higher dimensions, and how properties of these graphs can be exploited by computer algorithms. This project, supported by NSF Computing and Communication Foundations division and the Office of International Science and Engineering, provides matching funds for a Humboldt fellow from Germany, T. Ueckerdt, to spend a postdoctoral year working with Dr. Kobourov and his students at U of Arizona.

将硬币平放在桌子上，然后将它们推在一起。 记录硬币对给出了“接触图”。作为对象之间的录制连接的简单抽象非常强大：Internet上的计算机，锦标赛括号，社交网络和PERT图表都被用作图形。 具有几何实现的图形是在两个或多个维度中接触或相交对象具有特殊属性的图表（例如，可以绘制的图表已知80或40年，可以在没有交叉点的情况下绘制的图表可以作为硬币的接触图实现。通过计算机算法利用。 该项目得到了NSF计算与传播基础部门的支持以及国际科学与工程办公室，为来自德国T. Ueckerdt的洪堡研究员提供了匹配的资金，以与Kobourov博士及其学生在亚利桑那州U的学生一起度过博客一年。