Moving Vertices to Make Drawings Plane

  • Xavier Goaoc
  • Jan Kratochvíl
  • Yoshio Okamoto
  • Chan-Su Shin
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by moving vertices. In this paper we investigate the related problem MinMovedVertices which asks for the minimum number of vertex moves. First, we show that MinMovedVertices is NP-hard and hard to approximate. Second, we establish a connection to the graph-drawing problem 1BendPointSetEmbeddability, which yields similar results for that problem. Third, we give bounds for the behavior of MinMovedVertices on trees and general planar graphs.


Planar Graph Outer Face Outerplanar Graph Plane Drawing Polygonal Chain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xavier Goaoc
    • 1
  • Jan Kratochvíl
    • 2
  • Yoshio Okamoto
    • 3
  • Chan-Su Shin
    • 4
  • Alexander Wolff
    • 5
  1. 1.LORIAINRIA LorraineNancyFrance
  2. 2.Dept. Applied Math. and Inst. Theoret. Comp.ScienceCharles Univ.Czech Rep.
  3. 3.Dept. Information and Computer SciencesToyohashi Univ. of TechnologyJapan
  4. 4.School of Digital Inform. Eng.Hankuk Univ. of Foreign StudiesYonginKorea
  5. 5.Faculteit Wiskunde en InformaticaTU EindhovenThe Netherlands

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