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The minimum genus of a graph is an important question in graph theory and a key ingredient in several graph algorithms. However, its computation is NP-hard and turns out to be hard even in practice. Only recently, the first non-trivial approach -based on SAT and ILP (integer linear programming) models -has been presented, but it is unable to successfully tackle graphs of genus larger than 1 in practice. Herein, we show how to improve the ILP formulation. The crucial ingredients are two-fold.doi:10.4230/lipics.esa.2019.30 dblp:conf/esa/ChimaniW19 fatcat:2i4um2osnrbirlmslyachvi5ky