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DOI: 10.4230/LIPIcs.SEA.2018.22
Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments

Authors: Markus Chimani, Ivo Hedtke, and Tilo Wiedera

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
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.
Cite as

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)

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@InProceedings{chimani_et_al:LIPIcs.SEA.2018.22,
  author =	{Chimani, Markus and Hedtke, Ivo and Wiedera, Tilo},
  title =	{{Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.22},
  URN =		{urn:nbn:de:0030-drops-89572},
  doi =		{10.4230/LIPIcs.SEA.2018.22},
  annote =	{Keywords: maximum planar subgraph, integer linear programming, pseudo boolean satisfiability, graph drawing, algorithm engineering}
}
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