Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast

Authors Markus Chimani , Tilo Wiedera

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Markus Chimani
  • Theoretical Computer Science, Osnabrück University, Germany
Tilo Wiedera
  • Theoretical Computer Science, Osnabrück University, Germany

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Markus Chimani and Tilo Wiedera. Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph H of a given graph G such that H has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear programming and Kuratowski's famous planarity criterion. We build upon this approach and present new constraint classes - together with a lifting of the polyhedron - to obtain provably stronger LP-relaxations, and in turn faster algorithms in practice. The new constraints take Euler's polyhedron formula as a starting point and combine it with considering cycles in G. This paper discusses both the theoretical as well as the practical sides of this strengthening.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Graph theory
  • Theory of computation → Linear programming
  • algorithm engineering
  • graph algorithms
  • integer linear programming
  • maximum planar subgraph


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