On Compact RAC Drawings

Authors Henry Förster , Michael Kaufmann

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Author Details

Henry Förster
  • Wilhelm-Schickard-Institut für Informatik, University of Tübingen, Germany
Michael Kaufmann
  • Wilhelm-Schickard-Institut für Informatik, University of Tübingen, Germany


We thank Patrizio Angelini for useful discussions and proofreading and the anonymous referees of an earlier version for helpful comments.

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Henry Förster and Michael Kaufmann. On Compact RAC Drawings. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We present new bounds for the required area of Right Angle Crossing (RAC) drawings for complete graphs, i.e. drawings where any two crossing edges are perpendicular to each other. First, we improve upon results by Didimo et al. [Walter Didimo et al., 2011] and Di Giacomo et al. [Emilio Di Giacomo et al., 2011] by showing how to compute a RAC drawing with three bends per edge in cubic area. We also show that quadratic area can be achieved when allowing eight bends per edge in general or with three bends per edge for p-partite graphs. As a counterpart, we prove that in general quadratic area is not sufficient for RAC drawings with three bends per edge.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graphs and surfaces
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph algorithms
  • Human-centered computing → Graph drawings
  • RAC drawings
  • visualization of dense graphs
  • compact drawings


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