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  • 标题:Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast
  • 本地全文:下载
  • 作者:Markus Chimani ; Tilo Wiedera
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:112
  • 页码:1-14
  • DOI:10.4230/LIPIcs.ESA.2018.19
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要: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.
  • 关键词:algorithm engineering; graph algorithms; integer linear programming; maximum planar subgraph
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