Non-planar orthogonal drawings with fixed topology

  • Authors:

  • Markus Chimani;Gunnar W. Klau;René Weiskircher

  • Affiliations:

  • Institute of Computer Graphics and Algorithms, Vienna University of Technology, Austria;Institute of Computer Graphics and Algorithms, Vienna University of Technology, Austria;Institute of Computer Graphics and Algorithms, Vienna University of Technology, Austria

  • Venue:
  • SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
  • Year:
  • 2005

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Abstract

This paper discusses the calculation of bend minimal shapes for non-planar graphs with given topology. Based on the Simple-Kandinsky drawing standard – a simplification of the more complex Kandinsky standard – we show the disadvantage of using standard models for this task: We show that the minimal bend count is suboptimal, when these models are applied to non-planar graphs; it is therefore beneficial to extend these standards. We define such an extension for Simple-Kandinsky called Skanpag (Simple-Kandinsky for Non-Planar Graphs). It treats edge crossings in a special way by letting them share identical grid points where appropriate. Hence it allows crossings of whole bundles of edges instead of single edges only. Besides having a reduced number of bends, drawings following this standard are easier to read and consume less area than those produced by the traditional approaches. In this paper, we show a sharp upper bound of the bend count, if the standard Simple-Kandinsky model is used to calculate shapes for non-planar graphs. Furthermore, we present an algorithm that computes provably bend-minimal drawings in the Skanpag standard.