Skip to main content

Hans Bodlaender and the Theory of Kernelization Lower Bounds

  • Chapter
  • First Online:
Treewidth, Kernels, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12160))

  • 741 Accesses

Abstract

In this short letter I give a brief subjective account of my favorite result with Hans – our kernelization lower bounds framework. The purpose of this manuscript is not to give a formal introduction to this result and the area that spawned from it, nor is it meant to be a comprehensive survey of all related and relevant results. Rather, my aim here is to informally describe the history that lead to this result from a personal perspective, and to outline Hans’s role in the development of this theory into what it is today.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On problems without polynomial kernels. J. Comput. Syst. Sci. 75(8), 423–434 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Kernel bounds for path and cycle problems. Theor. Comput. Sci. 511, 117–136 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Preprocessing for treewidth: a combinatorial analysis through kernelization. SIAM J. Discrete Math. 27(4), 2108–2142 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Kernelization lower bounds by cross-composition. SIAM J. Discrete Math. 28(1), 277–305 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bodlaender, H.L., Thomassé, S., Yeo, A.: Kernel bounds for disjoint cycles and disjoint paths. Theor. Comput. Sci. 412(35), 4570–4578 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cygan, M., Grandoni, F., Hermelin, D.: Tight kernel bounds for problems on graphs with small degeneracy. ACM Trans. Algorithms 13(3), 43:1–43:22 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dell, H., Marx, D.: Kernelization of packing problems. In: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 68–81 (2012)

    Google Scholar 

  8. Dell, H., van Melkebeek, D.: Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses. J. ACM 61(4), 23:1–23:27 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dom, M., Lokshtanov, D., Saurabh, S.: Kernelization lower bounds through colors and ids. ACM Trans. Algorithms 11(2), 13 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Drucker, A.: New limits to classical and quantum instance compression. SIAM J. Comput. 44(5), 1443–1479 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fedor, F.V., Lokshtanov, D., Saurabh, S., Zehavi, M.: Kernelization Theory of Parameterized Preprocessing. Cambridge University Press, Cambridge (2019)

    MATH  Google Scholar 

  12. Fortnow, L., Santhanam, R.: Infeasibility of instance compression and succinct PCPs for NP. J. Comput. Syst. Sci. 77(1), 91–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hermelin, D., Kratsch, S., Soltys, K., Wahlström, M., Xi, W.: A completeness theory for polynomial (turing) kernelization. Algorithmica 71(3), 702–730 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hermelin, D., Wu, X.: Weak compositions and their applications to polynomial lower bounds for kernelization. In: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 104–113 (2012)

    Google Scholar 

  15. Kratsch, S.: Co-nondeterminism in compositions: a kernelization lower bound for a ramsey-type problem. ACM Trans. Algorithms 10(4), 19:1–19:16 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lokshtanov, D., Panolan, F., Ramanujan, M.S., Saurabh, S.: Lossy kernelization. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (STOC), pp. 224–237 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Danny Hermelin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hermelin, D. (2020). Hans Bodlaender and the Theory of Kernelization Lower Bounds. In: Fomin, F.V., Kratsch, S., van Leeuwen, E.J. (eds) Treewidth, Kernels, and Algorithms. Lecture Notes in Computer Science(), vol 12160. Springer, Cham. https://doi.org/10.1007/978-3-030-42071-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-42071-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-42070-3

  • Online ISBN: 978-3-030-42071-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics