Project Details
Projekt
Arrangements and Drawings
Subject Area
Theoretical Computer Science
Term
from 2018 to 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 340403547
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.
DFG Programme
Research Grants
International Connection
Austria, Switzerland
