Morphing Planar Graphs While Preserving Edge Directions

  • Therese Biedl
  • Anna Lubiw
  • Michael J. Spriggs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

Two straight-line drawings P,Q of a graph (V,E) are called parallel if, for every edge (u,v) ∈ E, the vector from u to v has the same direction in both P and Q. We study problems of the form: given simple, parallel drawings P,Q does there exist a continuous transformation between them such that intermediate drawings of the transformation remain simple and parallel with P (and Q)? We prove that a transformation can always be found in the case of orthogonal drawings; however, when edges are allowed to be in one of three or more slopes the problem becomes NP-hard.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Therese Biedl
    • 1
  • Anna Lubiw
    • 1
  • Michael J. Spriggs
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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