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Axis-Parallel Right Angle Crossing Graphs

Authors Patrizio Angelini , Michael A. Bekos , Julia Katheder , Michael Kaufmann , Maximilian Pfister , Torsten Ueckerdt

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Computational geometry
Keywords
  • Graph drawing
  • RAC graphs
  • Graph drawing algorithms

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Abstract

A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. 
In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.

Cite As Get BibTex

Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt. Axis-Parallel Right Angle Crossing Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.9

Author Details

Patrizio Angelini
  • John Cabot University, Rome, Italy
Michael A. Bekos
  • Department of Mathematics, University of Ioannina, Greece
Julia Katheder
  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Michael Kaufmann
  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Maximilian Pfister
  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Torsten Ueckerdt
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany

Funding

The work of J. Katheder and M. Kaufmann is supported by DFG grant Ka 812-18/2.

References

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