Bend-optimal orthogonal graph drawing in the general position model

  • Authors:

  • Stefan Felsner;Michael Kaufmann;Pavel Valtr

  • Affiliations:

  • Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany;Department of Applied Mathematics and Institute for Theoretical Comp. Sci. (CE-ITI), Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2014

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Abstract

We consider orthogonal drawings in the general position model, i.e., no two points share a coordinate. The drawings are also required to be bend minimal, i.e., each edge of a drawing in k dimensions has exactly one segment parallel to each coordinate direction that are glued together at k-1 bends. We provide a precise description of the class of graphs that admit an orthogonal drawing in the general position model in the plane. The main tools for the proof are Eulerian orientations of graphs and discrete harmonic functions. The tools developed for the planar case can also be applied in higher dimensions. We discuss two-bend drawings in three dimensions and show that K"2"k"+"2 admits a k-bend drawing in k+1 dimensions. If we allow that a vertex is placed at infinity, we can draw K"2"k"+"3 with k bends in k+1 dimensions.