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)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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