Beyond-planarity: A generalization of the planarity concept in graph drawing

超越平面性：图形绘制中平面性概念的概括

• 批准号: 364468267
• 负责人: Professor Dr. Michael Kaufmann, Ph.D.
• 金额: --
• 依托单位: Fachbereich IV: Informatik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/364468267?language=en
• 关键词: Beyond; planarity; generalization; concept; graph

The research field of graphs beyond planarity has been developed in recent years tremendously; evidence are several workshops and Dagstuhl seminars with this particular topic, as well as a survey book that will be published soon. In the first proposal in 2017, we gave a wide collection of research tasks in various directions. Meanwhile, we contributed in several directions; we summarized this in the progress report. However, we have also identified several new interesting research challenges and directions that we want to follow.1. Classification: We want robust definitions that are also parametrizable (fan-planar -> k-fan-planar, k-gap-planar -> (k,l)-gap-planar). We also want clear hierarchies between different graph classes. We expect to find new classes that complete the hierarchic structure. The classification will also be accompanied by combinatorial and algorithmic analyses on structural properties and parameters (e.g., low degree, girth etc) of the considered classes. 2. Layout: During the first project phase, we observed that the work on layout algorithms for graphs beyond planarity is very limited. The main reason for this is that the known techniques cannot be adopted so easily. Therefore, during the second project phase we will put our main focus on this aspect. For example for the standard approach to compute an appropriate topological embedding, and then a corresponding geometric embedding, both steps are challenging for the case of graphs beyond planarity and provide a considerable portion of risk in the project. To find algorithms which are practically applicable, we plan to provide fast exponential-time algorithms, maybe refined by parametrization, or efficient heuristics that can produce close-to-optimal layouts. It is definitely a far-from-trivial task to find corresponding requirements for more complex classes. Only elementary results are currently known mostly limited to the class of 1-planar graphs.3. Dissemination: By organizing meetings with other groups, we will develop the field further keeping the topic of beyond planarity as a central topic in regular workshops such as GNV in Heiligkreuztal, BWGD in Bertinoro and Dagstuhl. At such workshops, we find new insights by combining forces with people from combinatorial graph theory and computational geometry but also from algorithmic graph theory (e.g., Pach, T\'oth, Hoffmann, Speckmann). In 2016 and 2019, the applicant co-organized two Dagstuhl seminars on beyond planarity. A new edition of this successful Dagstuhl seminar is currently under consideration. As a side note, we further mention that in 2021 our group will be organizing the 29th Symposium of Graph Drawing and Network Visualization in Tübingen, a great honor and appreciation of our work in the field.

近年来，超出平面图的研究领域与这个特定的主题以及一本将在2017年的第一个提案中发表的调查书。各种说明。 。 ，我们观察到超出平面图的算法是有限的为了计算适当的拓扑嵌入，超出平面的图形的几何嵌入项目中的相当多的风险是找到实用的算法，这些算法是快速指示的算法，可能是通过参数化或效率启发的算法 - 目前，要查找复杂类的相应申报表。和Dagstuhl。我们。在2021年，我们的小组将在图宾根组织第29次图形图和网络可视化，这是对我们在该领域工作的巨大荣誉和欣赏。