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FPT Algorithms for Plane Completion Problems

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

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  • completion problems
  • FPT
  • plane graphs
  • topological isomorphism

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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) https://doi.org/10.4230/LIPIcs.MFCS.2016.26

Author Details

Dimitris Chatzidimitriou
Archontia C. Giannopoulou
Spyridon Maniatis
Clément Requilé
Dimitrios M. Thilikos
Dimitris Zoros

References

  1. Isolde Adler, Frederic Dorn, Fedor V. Fomin, Ignasi Sau, and Dimitrios M. Thilikos. Fast minor testing in planar graphs. Algorithmica, 64(1):69-84, 2012. Google Scholar
  2. Isolde Adler, Stavros G. Kolliopoulos, and Dimitrios M. Thilikos. Planar disjoint-paths completion. In Dániel Marx and Peter Rossmanith, editors, Parameterized and Exact Computation - 6th International Symposium, IPEC 2011, Saarbrücken, Germany, September 6-8, 2011. Revised Selected Papers, volume 7112 of Lecture Notes in Computer Science, pages 80-93. Springer, 2011. Google Scholar
  3. Ivan Bliznets, Fedor V. Fomin, Marcin Pilipczuk, and Michal Pilipczuk. A subexponential parameterized algorithm for proper interval completion. In Algorithms - ESA 2014 - 22th Annual European Symposium, Wroclaw, Poland, September 8-10, 2014. Proceedings, pages 173-184, 2014. Google Scholar
  4. V. Chvatal. Hamiltonian cycles. In E.L. Lawler, J.K. Lenstra, A.H.G.Rinnooy Kan, and D.B. Shmoys (Eds.), editors, The Traveling Salesman Problem, pages 403-429. Wiley, New York, 1985. Google Scholar
  5. Bruno Courcelle. The monadic second-order logic of graphs III: tree-decompositions, minor and complexity issues. ITA, 26:257-286, 1992. Google Scholar
  6. Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics. Springer, 2012. Google Scholar
  7. Michael B. Dillencourt. Finding hamiltonian cycles in delaunay triangulations is np-complete. Discrete Applied Mathematics, 64(3):207 - 217, 1996. Google Scholar
  8. Pål Grønås Drange, Fedor V. Fomin, Michal Pilipczuk, and Yngve Villanger. Exploring subexponential parameterized complexity of completion problems. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), STACS 2014, March 5-8, 2014, Lyon, France, pages 288-299, 2014. Google Scholar
  9. Haim Kaplan, Ron Shamir, and Robert Endre Tarjan. Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM J. Comput., 28(5):1906-1922, 1999. Google Scholar
  10. Bojan Mohar and Carsten Thomassen. Graphs on Surfaces. Johns Hopkins series in the mathematical sciences. Johns Hopkins University Press, 2001. Google Scholar
  11. Yngve Villanger, Pinar Heggernes, Christophe Paul, and Jan Arne Telle. Interval completion is fixed parameter tractable. SIAM J. Comput., 38(5):2007-2020, 2009. Google Scholar
  12. Hassler Whitney. Congruent graphs and the connectivity of graphs. American Journal of Mathematics, 54(1):pp. 150-168, 1932. Google Scholar
  13. M. Yannakakis. Computing the minimum fill-in is np-complete. SIAM Journal on Algebraic Discrete Methods, 2(1):77-79, 1981. Google Scholar
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