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)

Abstract

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.

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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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