Understanding Geometric Arrangements: Unions and Beyond

理解几何排列：并集及其他

• 批准号: 0830691
• 负责人: Boris Aronov
• 金额: $ 20万
• 依托单位: Polytechnic University of New York
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830691&HistoricalAwards=false
• 关键词: Understanding; Geometric; Arrangements; Unions; Beyond

Proposal: CCF- 0830691Institution: Polytechnic University of New YorkPI: Aronov, BorisTitle: Understanding Geometric Arrangements: Unions and Beyond ABSTRACTThe research centers on a class of geometric problems involving unions of objects. A variety of much-studied problems in combinatorial and computational geometry can be cast in these terms. Building on significant previous experience investigating the connections between combinatorics and algorithmics, the investigators explore combinatorial problems arising in the union-of-objects questions in order to develop new, simple, and powerful combinatorial tools and to refine those already available. Refining the techniques developed so far, the work expands the scope of problems to encompass questions of optimization in overlays of objects.Throughout the investigation, the researchers emphasize the following theme: Developing new, more powerful tools for dealing with combinatorial problems. Discovery of easier proofs of and streamlined approaches to ``classical'' problems makes research results significantly more accessible to students and non-specialists and ultimately more relevant to its claimed beneficiaries, the practitioners in the application areas. Moreover, they are very likely to foster further progress in the field.

提案：CCF-0830691机构：纽约理工大学PI：Aronov，Boris题目：理解几何排列：并集及其他摘要研究中心是一类涉及对象并集的几何问题。 在组合几何和计算几何中的许多研究问题都可以用这些术语来描述。 建立在以前的重要经验调查组合学和算法之间的联系，研究人员探索组合问题中出现的对象的联合问题，以开发新的，简单的，功能强大的组合工具，并完善那些已经可用。 改进了迄今为止开发的技术，这项工作扩大了问题的范围，包括对象覆盖的优化问题。在整个调查过程中，研究人员强调以下主题：开发新的，更强大的工具来处理组合问题。 发现“经典”问题的更简单证明和简化方法，使学生和非专业人员更容易获得研究结果，并最终与其声称的受益者，即应用领域的从业者更相关。此外，它们很可能促进这一领域的进一步进展。