Dagstuhl Seminar 24062
Beyond-Planar Graphs: Models, Structures and Geometric Representations
( Feb 04 – Feb 09, 2024 )
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https://www.dagstuhl.de/24062
Organizers
- Vida Dujmovic (University of Ottawa, CA)
- Seok-Hee Hong (The University of Sydney, AU)
- Michael Kaufmann (Universität Tübingen, DE)
- János Pach (Alfréd Rényi Institute - Budapest, HU & EPFL - Lausanne, CH)
Contact
- Andreas Dolzmann (for scientific matters)
- Christopher Michels (for administrative matters)
Many big data sets in various application domains have complex relationships, which can be modelled as graphs, consisting of entities and relationships between them. Consequently, graphs are extensively studied in both Mathematics and Computer science.
In particular, planar graphs, which can be drawn without edge crossings in the plane, form a distinguished role in Graph Theory and Graph Algorithms. Many structural properties of planar graphs are investigated, in terms of excluded minors, low density, and small separators, which lead to efficient algorithms for planar graphs. Consequently, fundamental algorithms for planar graphs have been discovered.
However, most real-world graphs, such as social networks and biological networks, are nonplanar. For example, the scale-free networks, which are used to model web graphs, social networks and biological networks, are globally sparse nonplanar graphs, with locally dense clusters and low diameters. To understand such real-world networks, we need to solve fundamental mathematical and algorithmic research questions on beyond-planar graphs, which generalize the notion of planar graphs, in terms of topological constraints or forbidden edge crossing patterns.
This Dagstuhl Seminar will investigate beyond-planar graphs, in particular, their combinatorial and topological structures (i.e., density, thickness, crossing pattern, chromatic number, queue number, and stack number), computational complexity and algorithmics for recognition, geometric representations (i.e., straight-line drawing, polyline drawing, intersection graphs), and their applications to real-world network visualization. Behind the fundamental scientific challenges and significant advances of this seminar lies the pragmatic need for effective visualization algorithms of real-world big complex networks.
Creative Commons BY 4.0
Vida Dujmovic, Seok-Hee Hong, Michael Kaufmann, and János Pach
Related Seminars
Classification
- Computational Geometry
- Data Structures and Algorithms
- Discrete Mathematics
Keywords
- Graph drawing
- Graph algorithm
- Graph theory
- Combinatorial geometry
- Network visualization
