REPORTS IN INFORMATICS

ISSN 0333-3590 Graph searching, elimination trees, and ageneralization of bandwidt

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 \textit{st}-orientation, area-minimal (bar-\textit{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