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Constrained Point-Set Embeddability of Planar Graphs

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Henk Meijer
  • Stephen Wismath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

This paper starts the investigation of a constrained version of the point-set embeddability problem. Let G = (V,E) be a planar graph with n vertices, G′ = (V′,E′) a subgraph of G, and S a set of n distinct points in the plane. We study the problem of computing a point-set embedding of G on S subject to the constraint that G′ is drawn with straight-line edges. Different drawing algorithms are presented that guarantee small curve complexity of the resulting drawing, i.e. a small number of bends per edge. It is proved that: (i) If G′ is an outerplanar graph and S is any set of points in convex position, a point-set embedding of G on S can be computed such that the edges of E ∖ E′ have at most 4 bends each. (ii) If S is any set of points in general position and G′ is a face of G or if it is a simple path, the curve complexity of the edges of E ∖ E′ is at most 8. (iii) If S is in general position and G′ is a set of k disjoint paths, the curve complexity of the edges of E ∖ E′ is O(2 k ).

Keywords

Planar Graph Disjoint Path Outerplanar Graph External Face Extra Point 
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 2009

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Henk Meijer
    • 2
  • Stephen Wismath
    • 3
  1. 1.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di PerugiaItaly
  2. 2.Roosevelt AcademyThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceUniversity of LethbridgeCanada

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