Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments

Authors Markus Chimani , Ivo Hedtke , Tilo Wiedera

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Author Details

Markus Chimani
  • Theoretical Computer Science, Osnabrück University, Germany
Ivo Hedtke
  • Data Strategy & Analytics, Schenker AG, Essen, Germany
Tilo Wiedera
  • Theoretical Computer Science, Osnabrück University, Germany

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Markus Chimani, Ivo Hedtke, and Tilo Wiedera. Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Given a graph G, the NP-hard Maximum Planar Subgraph problem asks for a planar subgraph of G with the maximum number of edges. The only known non-trivial exact algorithm utilizes Kuratowski's famous planarity criterion and can be formulated as an integer linear program (ILP) or a pseudo-boolean satisfiability problem (PBS). We examine three alternative characterizations of planarity regarding their applicability to model maximum planar subgraphs. For each, we consider both ILP and PBS variants, investigate diverse formulation aspects, and evaluate their practical performance.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • maximum planar subgraph
  • integer linear programming
  • pseudo boolean satisfiability
  • graph drawing
  • algorithm engineering


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