A Polynomial Kernel for Diamond-Free Editing

Authors Yixin Cao , Ashutosh Rai, R. B. Sandeep, Junjie Ye



PDF
Thumbnail PDF

File

LIPIcs.ESA.2018.10.pdf
  • Filesize: 0.49 MB
  • 13 pages

Document Identifiers

Author Details

Yixin Cao
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
Ashutosh Rai
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
R. B. Sandeep
  • Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Hungary
  • and Indian Institute of Technology Dharwad, Dharwad, India
Junjie Ye
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

Cite AsGet BibTex

Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye. A Polynomial Kernel for Diamond-Free Editing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ESA.2018.10

Abstract

Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Kernelization
  • Diamond-free
  • H-free editing
  • Graph modification problem

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. N. R. Aravind, R. B. Sandeep, and Naveen Sivadasan. Dichotomy results on the hardness of H-free edge modification problems. SIAM Journal on Discrete Mathematics, 31(1):542-561, 2017. Google Scholar
  2. Leizhen Cai. Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letter, 58(4):171-176, 1996. Google Scholar
  3. Leizhen Cai and Yufei Cai. Incompressibility of H-free edge modification problems. Algorithmica, 71(3):731-757, 2015. Google Scholar
  4. Yufei Cai. Polynomial kernelisation of H-free edge modification problems. Mphil thesis, Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China, 2012. Google Scholar
  5. Yixin Cao and Jianer Chen. Cluster editing: Kernelization based on edge cuts. Algorithmica, 64(1):152-169, 2012. Google Scholar
  6. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Undergraduate texts in computer science. Springer, 2013. Google Scholar
  7. Ehab S. El-Mallah and Charles J. Colbourn. The complexity of some edge deletion problems. IEEE Transactions on Circuits and Systems, 35(3):354-362, 1988. Google Scholar
  8. Paul Erdős and Richard Rado. Intersection theorems for systems of sets. Journal of the London Mathematical Society, 35(1):85-90, 1960. Google Scholar
  9. Jörg Flum and Martin Grohe. Parameterized Complexity Theory. Springer, 2006. Google Scholar
  10. Sylvain Guillemot, Frédéric Havet, Christophe Paul, and Anthony Perez. On the (non-) existence of polynomial kernels for P_l-free edge modification problems. Algorithmica, 65(4):900-926, 2013. Google Scholar
  11. Russell Impagliazzo and Ramamohan Paturi. On the complexity of k-SAT. Journal of Computer and System Sciences, 62(2):367-375, 2001. Google Scholar
  12. Stefan Kratsch and Magnus Wahlström. Two edge modification problems without polynomial kernels. Discrete Optimization, 10(3):193-199, 2013. Google Scholar
  13. John M. Lewis and Mihalis Yannakakis. The node-deletion problem for hereditary properties is NP-complete. Journal of Computer and System Sciences, 20(2):219-230, 1980. Google Scholar
  14. R. B. Sandeep and Naveen Sivadasan. Parameterized Lower Bound and Improved Kernel for Diamond-free Edge Deletion. In 10th International Symposium on Parameterized and Exact Computation, volume 43 of LIPIcs, pages 365-376. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2015. Google Scholar
  15. Mihalis Yannakakis. Edge-deletion problems. SIAM Journal on Computing, 10(2):297-309, 1981. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail