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Smooth Orthogonal Drawings of Planar Graphs

  • Muhammad Jawaherul Alam
  • Michael A. Bekos
  • Michael Kaufmann
  • Philipp Kindermann
  • Stephen G. Kobourov
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

In smooth orthogonal layouts of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal layouts of low edge complexity, that is, with few segments per edge. We say that a graph has smooth complexity k—for short, an SC k -layout—if it admits a smooth orthogonal drawing of edge complexity at most k.

Our main result is that every 4-planar graph has an SC2-layout. While our drawings may have super-polynomial area, we show that for 3-planar graphs, cubic area suffices. We also show that any biconnected 4-outerplane graph has an SC1-layout. On the negative side, we demonstrate an infinite family of biconnected 4-planar graphs that require exponential area for an SC1-layout. Finally, we present an infinite family of biconnected 4-planar graphs that do not admit an SC1-layout.

Keywords

Outer Face Horizontal Segment Biconnected Component Edge Complexity Free Port 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Muhammad Jawaherul Alam
    • 1
  • Michael A. Bekos
    • 2
  • Michael Kaufmann
    • 2
  • Philipp Kindermann
    • 3
  • Stephen G. Kobourov
    • 1
  • Alexander Wolff
    • 3
  1. 1.Department of Computer ScienceUniversity of ArizonaUSA
  2. 2.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenGermany
  3. 3.Lehrstuhl für Informatik IUniversität WürzburgGermany

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