Graphs with large total angular resolution

  title={Graphs with large total angular resolution},
  author={Oswin Aichholzer and Matias Korman and Yoshio Okamoto and Irene Parada and Daniel Perz and Andr{\'e} van Renssen and Birgit Vogtenhuber},
  booktitle={Graph Drawing},
The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove that, up… 

The Stub Resolution of 1-Planar Graphs

This paper investigates the stub resolution, a recently introduced criterion for nonplanar drawings, and considers 1-planar graphs and explores scenarios in which near optimal stub resolution can be obtained in drawings with zero, one, or two bends per edge.

Beyond Planar Graphs: Communications of NII Shonan Meetings

This chapter introduces various types of beyond planar graphs and briefly review known results on the edge density, computational complexity, and algorithms for testing beyondPlanar graphs.

Angular Resolutions: Around Vertices and Crossings

  • Y. Okamoto
  • Computer Science, Mathematics
    Beyond Planar Graphs
  • 2020



Maximizing the Total Resolution of Graphs

The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings).

Drawing graphs in the plane with high resolution

It is shown that the problem of deciding if R=2 pi /d for a graph is NP-hard for d=4, and a counting argument is used to show that R=O(log d/d/sup 2/) for many graphs.

A Heuristic Approach towards Drawings of Graphs with High Crossing Resolution

The experimental evaluation indicates that the new heuristic produces drawings with better crossing resolution, but this comes at the cost of slightly higher edge-length ratio, especially when the input graph is large.

Drawing graphs with right angle crossings

This paper studies the interplay between number of bends per edge and total number of edges in RAC drawings to establish upper and lower bounds on these quantities.

Notes on Large Angle Crossing Graphs

Upper and lower bounds for the number of edges in aAC graphs for all 0 < a < Pi/2 are given.

The Quality Ratio of RAC Drawings and Planar Drawings of Planar Graphs

We study how much better a right-angled crossing (RAC) drawing of a planar graph can be than any planar drawing of the same planar graph. We analyze the area requirement, the edge-length ratio, and

The Straight-Line RAC Drawing Problem is NP-Hard

Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are

Effects of Crossing Angles

It was found that the effect varied with the size of crossing angles, and task response time decreased as the crossing angle increased, and the rate of the decrease tended to level off when the angle was close to 90 degrees.

Using eye tracking to investigate graph layout effects

  • Weidong Huang
  • Computer Science
    2007 6th International Asia-Pacific Symposium on Visualization
  • 2007
A preliminary eye tracking experiment was conducted to test the effects of crossing angles and geometric-path tendency on eye movements and performance, showing that small angles can slow down and trigger extra eye movements, causing delays for path search tasks, whereas crossings have little impact on node locating tasks.