Embedding Four-Directional Paths on Convex Point Sets

  • Oswin Aichholzer
  • Thomas Hackl
  • Sarah Lutteropp
  • Tamara Mchedlidze
  • Birgit Vogtenhuber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


A directed path whose edges are assigned labels “up”, “down”, “right”, or “left” is called four-directional, and three-directional if at most three out of the four labels are used. A direction-consistent embedding of an n-vertex four-directional path P on a set S of n points in the plane is a straight-line drawing of P where each vertex of P is mapped to a distinct point of S and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Oswin Aichholzer
    • 1
  • Thomas Hackl
    • 1
  • Sarah Lutteropp
    • 2
  • Tamara Mchedlidze
    • 2
  • Birgit Vogtenhuber
    • 1
  1. 1.Institute for Software TechnologyGraz University of TechnologyAustria
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany

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