Stronger ILPs for the Graph Genus Problem

Markus Chimani, Tilo Wiedera, Michael Wagner
2019 European Symposium on Algorithms  
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.
more » ... st, we show that instead of modeling rotation schemes explicitly, it suffices to optimize over partitions of the (bidirected) arc set A of the graph. Second, we exploit the cycle structure of the graph, explicitly mapping short closed walks on A to faces in the embedding. Besides the theoretical advantages of our models, we show their practical strength by a thorough experimental evaluation. Contrary to the previous approach, we are able to quickly solve many instances of genus > 1. ACM Subject Classification Mathematics of computing → Graphs and surfaces; Mathematics of computing → Graph algorithms; Theory of computation → Linear programming Keywords and phrases algorithm engineering, genus, integer linear programming Digital Object Identifier 10.4230/LIPIcs.ESA.2019.30
doi:10.4230/lipics.esa.2019.30 dblp:conf/esa/ChimaniW19 fatcat:2i4um2osnrbirlmslyachvi5ky