# Experimental Analysis of the Accessibility of Drawings with Few Segments

@article{Kindermann2017ExperimentalAO, title={Experimental Analysis of the Accessibility of Drawings with Few Segments}, author={Philipp Kindermann and Wouter Meulemans and Andr{\'e} Schulz}, journal={ArXiv}, year={2017}, volume={abs/1708.09815} }

The visual complexity of a graph drawing is defined as the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges, e.g., one needs only one line segment to draw two collinear incident edges. We study the question if drawings with few segments have a better aesthetic appeal and help the user to asses the underlying graph. We design an experiment that investigates two different graph types (trees and sparse graphs), three different…

## 10 Citations

### Drawing planar graphs with few segments on a polynomial grid

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The visual complexity of a graph drawing can be measured by the number of geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are…

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- Mathematics, Computer ScienceWADS
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This work investigates the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes, and shows lower and upper bounds for the numbers of lines and planes needed for covering drawings of graphs in certain graph classes.

### Drawing Planar Graphs with Few Geometric Primitives

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The problem of drawing maximal planar graphs with circular arcs is studied and an algorithm to draw such graphs using only \((5n\,11)/3\) arcs is provided, providing a significant improvement over the lower bound of 2n for line segments for a nontrivial graph class.

### Drawing Graphs on Few Circles and Few Spheres

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It turns out that spherical covers are sometimes significantly smaller than affine covers, and this paper introduces the spherical cover number, which is the minimum number of circles that together cover a crossing-free circular-arc drawing in 2D (or 3D).

### Upward Planar Drawings with Three and More Slopes

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It is shown that in general NP-hard to decide whether a given directed graph with maximum in and outdegree at most k admits such a drawing with k slopes, and for cactus graphs deciding and constructing a drawing can be done in polynomial time.

### The Segment Number: Algorithms and Universal Lower Bounds for Some Classes of Planar Graphs

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The first linear universal lower bounds for outerpaths, maximal outerplanar graphs, 2-trees, and planar 3-Trees are proved, which shows that the existing algorithms for these graph classes are constant-factor approximations.

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### Level-Planar Drawings with Few Slopes

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It is shown that testing whether non-proper level graphs admit level-planar drawings with λ slopes is NP -hard even in restricted cases.

### Line and Plane Cover Numbers Revisited

- Mathematics, Computer ScienceGraph Drawing
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It is NP-hard to decide, for a given planar graph~$G, whether $\pi^1_2(G)=2$ and it is shown that the universal stacked triangulation of depth~$d$, $G_d, has $\pi+1(G-d)=d+1$.

### Upward Planar Drawings with Three Slopes

- Computer ScienceArXiv
- 2021

It is shown that deciding whether a digraph admits such a drawing is NP-hard already for embedded outerplanar digraphs, though linear-time solvable for trees with and without given embedding.

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