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A Polynomial Kernel for 3-Leaf Power Deletion

Authors Jungho Ahn, Eduard Eiben , O-joung Kwon , Sang-il Oum

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • 𝓁-leaf power
  • parameterized algorithms
  • kernelization

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Abstract

For a non-negative integer 𝓁, a graph G is an 𝓁-leaf power of a tree T if V(G) is equal to the set of leaves of T, and distinct vertices v and w of G are adjacent if and only if the distance between v and w in T is at most 𝓁. Given a graph G, 3-Leaf Power Deletion asks whether there is a set S ⊆ V(G) of size at most k such that G\S is a 3-leaf power of some treeT. We provide a polynomial kernel for this problem. More specifically, we present a polynomial-time algorithm for an input instance (G,k) to output an equivalent instance (G',k') such that k'≤ k and G' has at most O(k^14) vertices.

Cite As Get BibTex

Jungho Ahn, Eduard Eiben, O-joung Kwon, and Sang-il Oum. A Polynomial Kernel for 3-Leaf Power Deletion. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.5

Author Details

Jungho Ahn
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
Eduard Eiben
  • Department of Computer Science, Royal Holloway, University of London, Egham, UK
O-joung Kwon
  • Department of Mathematics, Incheon National University, South Korea
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
Sang-il Oum
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea

Funding

Jungho Ahn, O-joung Kwon, and Sang-il Oum: the Institute for Basic Science (IBS-R029-C1).
  • Kwon, O-joung: the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. NRF-2018R1D1A1B07050294).

References

  1. Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, and Meirav Zehavi. Feedback vertex set inspired kernel for chordal vertex deletion. ACM Trans. Algorithms, 15(1):Art. 11, 28, 2019. URL: https://doi.org/10.1145/3284356.
  2. Akanksha Agrawal, Pranabendu Misra, Saket Saurabh, and Meirav Zehavi. Interval vertex deletion admits a polynomial kernel. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1711-1730. SIAM, Philadelphia, PA, 2019. URL: https://doi.org/10.1137/1.9781611975482.103.
  3. Jungho Ahn. A polynomial kernel for 3-leaf power deletion. Master’s thesis, KAIST, South Korea, 2020. Google Scholar
  4. Vineet Bafna, Piotr Berman, and Toshihiro Fujito. A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Discrete Math., 12(3):289-297, 1999. URL: https://doi.org/10.1137/S0895480196305124.
  5. Andreas Brandstädt and Van Bang Le. Structure and linear time recognition of 3-leaf powers. Inform. Process. Lett., 98(4):133-138, 2006. URL: https://doi.org/10.1016/j.ipl.2006.01.004.
  6. Andreas Brandstädt, Van Bang Le, and R. Sritharan. Structure and linear-time recognition of 4-leaf powers. ACM Trans. Algorithms, 5(1):Art. 11, 22, 2009. URL: https://doi.org/10.1145/1435375.1435386.
  7. Yixin Cao and Dániel Marx. Chordal editing is fixed-parameter tractable. Algorithmica, 75(1):118-137, 2016. URL: https://doi.org/10.1007/s00453-015-0014-x.
  8. Maw-Shang Chang and Ming-Tat Ko. The 3-Steiner root problem. In Graph-theoretic concepts in computer science, volume 4769 of Lecture Notes in Comput. Sci., pages 109-120. Springer, Berlin, 2007. URL: https://doi.org/10.1007/978-3-540-74839-7_11.
  9. Jianer Chen, Iyad A. Kanj, and Ge Xia. Improved upper bounds for vertex cover. Theoret. Comput. Sci., 411(40-42):3736-3756, 2010. URL: https://doi.org/10.1016/j.tcs.2010.06.026.
  10. Bruno Courcelle, Johann A. Makowsky, and Udi Rotics. Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst., 33(2):125-150, 2000. URL: https://doi.org/10.1007/s002249910009.
  11. William H. Cunningham. Decomposition of directed graphs. SIAM J. Algebraic Discrete Methods, 3(2):214-228, 1982. URL: https://doi.org/10.1137/0603021.
  12. Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized algorithms. Springer, Cham, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  13. Reinhard Diestel. Graph theory, volume 173 of Graduate Texts in Mathematics. Springer, Heidelberg, fourth edition, 2010. URL: https://doi.org/10.1007/978-3-642-14279-6.
  14. Michael Dom, Jiong Guo, Falk Hüffner, and Rolf Niedermeier. Error compensation in leaf power problems. Algorithmica, 44(4):363-381, 2006. URL: https://doi.org/10.1007/s00453-005-1180-z.
  15. Rodney G. Downey and Michael R. Fellows. Fundamentals of parameterized complexity. Texts in Computer Science. Springer, London, 2013. URL: https://doi.org/10.1007/978-1-4471-5559-1.
  16. Guillaume Ducoffe. The 4-Steiner root problem. In Graph-theoretic concepts in computer science, volume 11789 of Lecture Notes in Comput. Sci., pages 14-26. Springer, Berlin, 2019. URL: https://doi.org/10.1007/978-3-030-30786-8_2.
  17. Eduard Eiben, Robert Ganian, and O-joung Kwon. A single-exponential fixed-parameter algorithm for distance-hereditary vertex deletion. J. Comput. System Sci., 97:121-146, 2018. URL: https://doi.org/10.1016/j.jcss.2018.05.005.
  18. David Eppstein and Elham Havvaei. Parameterized leaf power recognition via embedding into graph products. In 13th International Symposium on Parameterized and Exact Computation, volume 115 of LIPIcs. Leibniz Int. Proc. Inform., pages Art. No. 16, 14. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2019. Google Scholar
  19. J. Flum and M. Grohe. Parameterized complexity theory. Texts in Theoretical Computer Science. An EATCS Series. Springer-Verlag, Berlin, 2006. Google Scholar
  20. Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi. Subquadratic kernels for implicit 3-hitting set and 3-set packing problems. ACM Trans. Algorithms, 15(1):Art. 13, 44, 2019. URL: https://doi.org/10.1145/3293466.
  21. Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. Kernelization. Cambridge University Press, Cambridge, 2019. Theory of parameterized preprocessing. Google Scholar
  22. Frank Gurski and Egon Wanke. The NLC-width and clique-width for powers of graphs of bounded tree-width. Discrete Appl. Math., 157(4):583-595, 2009. URL: https://doi.org/10.1016/j.dam.2008.08.031.
  23. Falk Hüffner, Christian Komusiewicz, Hannes Moser, and Rolf Niedermeier. Fixed-parameter algorithms for cluster vertex deletion. Theory Comput. Syst., 47(1):196-217, 2010. URL: https://doi.org/10.1007/s00224-008-9150-x.
  24. Bart M. P. Jansen and Marcin Pilipczuk. Approximation and kernelization for chordal vertex deletion. SIAM J. Discrete Math., 32(3):2258-2301, 2018. URL: https://doi.org/10.1137/17M112035X.
  25. Eun Jung Kim and O-joung Kwon. A polynomial kernel for block graph deletion. Algorithmica, 79(1):251-270, 2017. URL: https://doi.org/10.1007/s00453-017-0316-2.
  26. Eun Jung Kim and O-joung Kwon. A polynomial kernel for distance-hereditary vertex deletion. In Algorithms and data structures, volume 10389 of Lecture Notes in Comput. Sci., pages 509-520. Springer, Cham, 2017. URL: https://doi.org/10.1007/978-3-319-62127-2_43.
  27. Michael Lampis. A kernel of order 2k-clog k for vertex cover. Inform. Process. Lett., 111(23-24):1089-1091, 2011. URL: https://doi.org/10.1016/j.ipl.2011.09.003.
  28. John M. Lewis and Mihalis Yannakakis. The node-deletion problem for hereditary properties is NP-complete. J. Comput. System Sci., 20(2):219-230, 1980. ACM-SIGACT Symposium on the Theory of Computing (San Diego, Calif., 1978). URL: https://doi.org/10.1016/0022-0000(80)90060-4.
  29. Daniel Lokshtanov, N. S. Narayanaswamy, Venkatesh Raman, M. S. Ramanujan, and Saket Saurabh. Faster parameterized algorithms using linear programming. ACM Trans. Algorithms, 11(2):Art. 15, 31, 2014. URL: https://doi.org/10.1145/2566616.
  30. Dániel Marx. Chordal deletion is fixed-parameter tractable. Algorithmica, 57(4):747-768, 2010. URL: https://doi.org/10.1007/s00453-008-9233-8.
  31. Naomi Nishimura, Prabhakar Ragde, and Dimitrios M. Thilikos. On graph powers for leaf-labeled trees. J. Algorithms, 42(1):69-108, 2002. URL: https://doi.org/10.1006/jagm.2001.1195.
  32. Dieter Rautenbach. Some remarks about leaf roots. Discrete Math., 306(13):1456-1461, 2006. URL: https://doi.org/10.1016/j.disc.2006.03.030.
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