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We present a simple and versatile formulation of grid-based graphrepresentation problems as an integer linear program (ILP) and a correspondingSAT instance. In a grid-based representation vertices and edges correspond toaxis-parallel boxes on an underlying integer grid; boxes can be furtherconstrained in their shapes and interactions by additional problem-specificconstraints. We describe a general d-dimensional model for grid representationproblems. 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 implementedSAT-models for all of the above problems and evaluated them on the Rome graphscollection. The experiments show that our model successfully solves NP-hardproblems within few minutes on small to medium-size Rome graphs.

Using ILP/SAT to determine pathwidth, visibility representations, and other grid-based graph drawings