1 research outputs found
Using ILP/SAT to determine pathwidth, visibility representations, and other grid-based graph drawings
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.Comment: Full version of GD 2013 pape