Skip to main content
SpringerLink
Log in

Kernelization, Partially Polynomial Kernels

  • Living reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 218 Accesses

Years and Authors of Summarized Original Work

2011; Betzler, Guo, Komusiewicz, Niedermeier

2013; Basavaraju, Francis, Ramanujan, Saurabh

2014; Betzler, Bredereck, Niedermeier

Problem Definition

In parameterized complexity, each instance (I, k) of a problem comes with an additional parameter k which describes structural properties of the instance, for example, the maximum degree of an input graph. A problem is called fixed-parameter tractable if it can be solved in f(k) ⋅poly(n) time, that is, the super-polynomial part of the running time depends only on k. Consequently, instances of the problem can be solved efficiently if k is small.

One way to show fixed-parameter tractability of a problem is the design of a polynomial-time data reduction algorithm that reduces any input instance (I, k) to one whose size is bounded in k. This idea is captured by the notion of kernelization.

Definition 1.

Let (I, k) be an instance of a parameterized problem P, where I ∈ Σ  ∗ denotes the input...

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

Access this chapter

Log in via an institution

Institutional subscriptions

Recommended Reading

  1. Basavaraju M, Francis MC, Ramanujan MS, Saurabh S (2013) Partially polynomial kernels for set cover and test cover. In: FSTTCS ’13, Guwahati. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik, LIPIcs, vol 24, pp 67–78

    Google Scholar 

  2. Betzler N, Guo J, Komusiewicz C, Niedermeier R (2011) Average parameterization and partial kernelization for computing medians. J Comput Syst Sci 77(4):774–789

    Article  MathSciNet  MATH  Google Scholar 

  3. Betzler N, Bredereck R, Niedermeier R (2014) Theoretical and empirical evaluation of data reduction for exact Kemeny rank aggregation. Auton Agents Multi-Agent Syst 28(5):721–748

    Article  Google Scholar 

  4. Bodlaender HL, Downey RG, Fellows MR, Hermelin D (2009) On problems without polynomial kernels. J Comput Syst Sci 75(8):423–434

    Article  MathSciNet  MATH  Google Scholar 

  5. Crowston R, Fellows M, Gutin G, Jones M, Kim EJ, Rosamond F, Ruzsa IZ, Thomassé S, Yeo A (2014) Satisfying more than half of a system of linear equations over GF(2): a multivariate approach. J Comput Syst Sci 80(4):687–696

    Article  MATH  Google Scholar 

  6. Fellows MR, Jansen BMP, Rosamond FA (2013) Towards fully multivariate algorithmics: parameter ecology and the deconstruction of computational complexity. Eur J Comb 34(3): 541–566

    Article  MathSciNet  MATH  Google Scholar 

  7. Komusiewicz C (2011) Parameterized algorithmics for network analysis: clustering & querying. PhD thesis, Technische Universität Berlin, Berlin

    Google Scholar 

  8. Komusiewicz C, Niedermeier R (2012) New races in parameterized algorithmics. In: MFCS ’12, Bratislava. Lecture notes in computer science, vol 7464. Springer, pp 19–30

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany

    Christian Komusiewicz

Authors
  1. Christian Komusiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Komusiewicz .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Komusiewicz, C. (2014). Kernelization, Partially Polynomial Kernels. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_530-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27848-8_530-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation