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DOI: 10.4230/LIPIcs.MFCS.2016.26
FPT Algorithms for Plane Completion Problems

Authors: Dimitris Chatzidimitriou, Archontia C. Giannopoulou, Spyridon Maniatis, Clément Requilé, Dimitrios M. Thilikos, and Dimitris Zoros

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
The Plane Subgraph (resp. Topological Minor) Completion problem asks, given a (possibly disconnected) plane (multi)graph Gamma and a connected plane (multi)graph Delta, whether it is possible to add edges in Gamma without violating the planarity of its embedding so that it contains some subgraph (resp. topological minor) that is topologically isomorphic to Delta. We give FPT algorithms that solve both problems in f(|E(Delta)|)*|E(\Gamma)|^{2} steps. Moreover, for the Plane Subgraph Completion problem we show that f(k)=2^{O(k*log(k))}.
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Dimitris Chatzidimitriou, Archontia C. Giannopoulou, Spyridon Maniatis, Clément Requilé, Dimitrios M. Thilikos, and Dimitris Zoros. FPT Algorithms for Plane Completion Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatzidimitriou_et_al:LIPIcs.MFCS.2016.26,
  author =	{Chatzidimitriou, Dimitris and Giannopoulou, Archontia C. and Maniatis, Spyridon and Requil\'{e}, Cl\'{e}ment and Thilikos, Dimitrios M. and Zoros, Dimitris},
  title =	{{FPT Algorithms for Plane Completion Problems}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.26},
  URN =		{urn:nbn:de:0030-drops-64418},
  doi =		{10.4230/LIPIcs.MFCS.2016.26},
  annote =	{Keywords: completion problems, FPT, plane graphs, topological isomorphism}
}
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