Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings

  • Therese Biedl
  • Thomas Bläsius
  • Benjamin Niedermann
  • Martin Nöllenburg
  • Roman Prutkin
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


We present a simple and versatile formulation of grid-based graph representation problems as an integer linear program (ILP) and a corresponding SAT instance. In a grid-based representation vertices and edges correspond to axis-parallel boxes on an underlying integer grid; boxes can be further constrained in their shapes and interactions by additional problem-specific constraints. We describe a general d-dimensional model for grid representation problems. This model can be used to solve a variety of NP-hard graph problems, including pathwidth, bandwidth, optimum st-orientation, area-minimal (bar-k) visibility representation, boxicity-k graphs and others. We implemented SAT-models for all of the above problems and evaluated them on the Rome graphs collection. The experiments show that our model successfully solves NP-hard problems within few minutes on small to medium-size Rome graphs.


Planar Graph Visibility Representation Integer Linear Programming Interval Graph Integer Linear Programming Model 
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 International Publishing Switzerland 2013

Authors and Affiliations

  • Therese Biedl
    • 1
  • Thomas Bläsius
    • 2
  • Benjamin Niedermann
    • 2
  • Martin Nöllenburg
    • 2
  • Roman Prutkin
    • 2
  • Ignaz Rutter
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany

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