FWF - ArrDra - Arrangements and Drawings

Arrangements of geometric objects and drawings of graphs lie at the core of modern Discrete and Computational Geometry. They serve as a exible tool in applications in both mathematics and computer science, since many important problems that involve geometric information may be modeled as problems on arrangements or graphs. Therefore, the study of these structures and a better understanding of their properties impacts a wide variety of problem domains. This DACH project \Arrangements and Drawings" connects groups that have already cooperated successfully in the European collaborative research programme EuroGIGA. In this follow-up project, we plan to investigate the relationships between different types of drawings and arrangements, as well as their abstract representations and their algorithmic properties. We have composed a list of challenging problems from the following four focus areas: (A) Arrangements of lines and pseudolines, (B) Drawings of graphs, (C) Structure of intersection, and (D) Planar and near-planar structures. The goal of this project is to gain insights in order to broaden our understanding of these areas and to jointly attack some of their long-standing open questions. These questions are notoriously diffcult though important, so that even partial solutions are expected to have impact.