%0 Conference Paper %1 hkms-dttfg-eurocg16 %A Hültenschmidt, Gregor %A Kindermann, Philipp %A Meulemans, Wouter %A Schulz, André %B Proceedings of the 32nd European Workshop on Computational Geometry (EuroCG'16) %D 2016 %E Barequet, Gill %E Papadopoulou, Evanthia %I Lugano %K drawing geometric myown primitives %P 55--58 %T Drawing Trees and Triangulations with Few Geometric Primitives %U http://www.eurocg2016.usi.ch/sites/default/files/EuroCG16-BookOfAbstract.pdf %X We define the visual complexity of a plane graph drawing to be the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g. you need only one line segment to draw two collinear edges of the same vertex). We show that trees can be drawn with $3n/4$ straight-line segments on a polynomial grid, and with $n/2$ straight-line segments on a quasi-polynomial grid. We also study the problem of drawing maximal triangulations with circular arcs and provide an algorithm to draw such graphs using only $(5n - 11)/3$ arcs. This provides a significant improvement over the lower bound of $2n$ for line segments for a nontrivial graph class.

@inproceedings{hkms-dttfg-eurocg16, abstract = {We define the \emph{visual complexity} of a plane graph drawing to be the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g. you need only one line segment to draw two collinear edges of the same vertex). We show that trees can be drawn with $3n/4$ straight-line segments on a polynomial grid, and with $n/2$ straight-line segments on a quasi-polynomial grid. We also study the problem of drawing maximal triangulations with circular arcs and provide an algorithm to draw such graphs using only $(5n - 11)/3$ arcs. This provides a significant improvement over the lower bound of $2n$ for line segments for a nontrivial graph class.}, added-at = {2016-05-30T13:07:41.000+0200}, arxiv = {https://arxiv.org/abs/1703.01691}, author = {H{\"u}ltenschmidt, Gregor and Kindermann, Philipp and Meulemans, Wouter and Schulz, Andr{\'e}}, biburl = {https://www.bibsonomy.org/bibtex/2144715671c4847b303dfd173b9b8d73a/kindermann}, booktitle = {Proceedings of the 32nd European Workshop on Computational Geometry (EuroCG'16)}, editor = {Barequet, Gill and Papadopoulou, Evanthia}, interhash = {c891edae3ae470d120c9e7335c03282f}, intrahash = {144715671c4847b303dfd173b9b8d73a}, keywords = {drawing geometric myown primitives}, month = mar, note = {Abstract}, pages = {55--58}, publisher = {Lugano}, slides = {http://www1.pub.informatik.uni-wuerzburg.de/pub/kindermann/slides/2016-eurocg-fewarcs.pdf}, timestamp = {2018-09-18T07:00:23.000+0200}, title = {Drawing Trees and Triangulations with Few Geometric Primitives}, url = {http://www.eurocg2016.usi.ch/sites/default/files/EuroCG16-BookOfAbstract.pdf}, year = 2016 }