A practical method for the minimum genus of a graph: Models and experiments

Abstract

We consider the problem of the minimum genus of a graph, a fundamental measure of non-planarity. We propose the first formulations of this problem as an integer linear program (ILP) and as a satisfiability problem (SAT). These allow us to develop the first working implementations of general algorithms for the problem, other than exhaustive search. We investigate several different ways to speed-up and strengthen the formulations; our experimental evaluation shows that our approach performs well on small to medium-sized graphs with small genus, and compares favorably to other approaches.