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arXiv · 1806.08283

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

Markus Chimani·Tilo Wiedera
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Abstract

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.

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Markus Chimani, Tilo Wiedera. 2018-06-21. Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast. https://arxiv.org/abs/1806.08283

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