Arrangements and Drawings
安排和图纸
基本信息
- 批准号:340403547
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2018
- 资助国家:德国
- 起止时间:2017-12-31 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Arrangements of geometric objects and drawings of graphs lie at the core ofmodern Discrete and Computational Geometry. They serve as a flexible tool inapplications in both mathematics and computer science, since many importantproblems that involve geometric information may be modeled as problems onarrangements or graphs. Therefore, the study of these structures and a betterunderstanding of their properties impacts a wide variety of problem domains.This DACH project connects groups that have already cooperated successfully inthe European collaborative research programme EuroGIGA. In this follow-upproject, we plan to investigate the relationships between different types ofdrawings and arrangements, as well as their abstract representations and theiralgorithmic properties. We have composed a list of challenging problems rangingfrom Erdös-Szekeres type questions via questions about the computational powerof sidedness predicates to questions about flip graphs. The backbone of theproject is structured into four focus areas. (A) Arrangements of lines and pseudolines. (B) Drawings of graphs. (C) Structure of intersection. (D) Planar and near-planar structures.The goal of this project is to gain insights in order to broaden ourunderstanding of these areas and to jointly attack some of their long-standingopen questions. These questions are notoriously difficult though important, sothat even partial solutions are expected to have impact. Each of the four sitesof the DACH project will concentrate efforts on a subset of the focus areassuch that research in each of these areas will be conducted in at least two ofthe four sites.
几何对象的排列和图形的绘制是现代离散几何和计算几何的核心。它们在数学和计算机科学的应用中都是一种灵活的工具,因为许多涉及几何信息的重要问题可以被建模为排列或图的问题。因此,对这些结构的研究和对其性质的更好理解影响着各种各样的问题领域。这个DACH项目将已经在欧洲合作研究计划EuroGIGA中成功合作的小组联系起来。在这个后续项目中,我们计划研究不同类型的图纸和排列之间的关系,以及它们的抽象表示和算法属性。我们编写了一个具有挑战性的问题列表,从Erdös-Szekeres类型的问题到关于边面性谓词的计算能力的问题,再到关于翻转图的问题。该项目的主干分为四个重点领域。(A)线和伪线的安排。(B)图表。(C)交叉口结构。(D)平面和近平面结构。该项目的目标是获得洞察力,以扩大我们对这些领域的理解,并共同解决一些长期存在的开放性问题。这些问题虽然很重要,但却是出了名的困难,所以即使是部分的解决方案也有望产生影响。DACH项目的四个站点中的每一个都将集中精力在重点领域的一个子集上,这样每个领域的研究将在四个站点中的至少两个站点进行。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Professor Dr. Stefan Felsner其他文献
Professor Dr. Stefan Felsner的其他文献
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{{ truncateString('Professor Dr. Stefan Felsner', 18)}}的其他基金
Combinatorics of Point Sets and Arrangements of Objects
点集组合和对象排列
- 批准号:
195353047 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Research Grants
Graphenorientierungen in Ebene und Raum
平面和空间中的图形方向
- 批准号:
55908010 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Research Grants
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