Proving or Disproving Planar Straight-Line Embeddability onto Given Rectangles

  • Michael Kaufmann
  • Stephan Kottler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)

Abstract

Given a plane graph G = (V,E) and a rectangle we ask whether there exists a planar straight-line embedding of G onto the grid-points of the rectangle. For this NP-hard problem [5] some powerful heuristics have been developed to minimise the area of an embedding of a given graph [5,4]. Moreover, for particular families of graphs upper and lower bounds on the area have been proven [2]. However, in the general case it is not possible to ensure whether there is an embedding that preserves a particular area restriction A = h ·w. We present an implementation based on a translation into SAT to tackle this kind of problems for small graphs. We only describe the direct encoding into CNF that turned out to be most suitable.

References

  1. 1.
    Open Graph Drawing Framework, http://www.ogdf.net
  2. 2.
    Frati, F., Patrignani, M.: A note on minimum area straight-line drawings of planar graphs. In: 15th International Symposium on Graph Drawing (2007)Google Scholar
  3. 3.
    Kottler, S.: Solver descriptions for the SAT competition (2009), satcompetition.orgGoogle Scholar
  4. 4.
    Krug, M.: Minimizing the area for planar straight-line grid drawings. Master’s thesis, University of Karlsruhe (2007)Google Scholar
  5. 5.
    Krug, M., Wagner, D.: Minimizing the area for planar straight-line grid drawings. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 207–212. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael Kaufmann
    • 1
  • Stephan Kottler
    • 1
  1. 1.Wilhelm–Schickard–InstituteUniversity of TübingenGermany

Personalised recommendations