Proportional Contact Representations of Planar Graphs

  • Muhammad Jawaherul Alam
  • Therese Biedl
  • Stefan Felsner
  • Michael Kaufmann
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Abstract

We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Muhammad Jawaherul Alam
    • 1
  • Therese Biedl
    • 2
  • Stefan Felsner
    • 3
  • Michael Kaufmann
    • 4
  • Stephen G. Kobourov
    • 1
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  2. 2.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Institut für MathematikTechnische Universität BerlinBerlinGermany
  4. 4.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenTübingenGermany

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