Skip to main content

Parameterized Approximation Algorithms for Hitting Set

  • Conference paper
Approximation and Online Algorithms (WAOA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7164))

Included in the following conference series:

Abstract

We are going to analyze simple search tree algorithms for approximating d -Hitting Set, focussing on the case of factor-2 approximations for d = 3. We also derive several results for hypergraph instances of bounded degree, including a new polynomial-time approximation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bar-Yehuda, R.: One for the price of two: a unified approach for approximating covering problems. Algorithmica 27, 131–144 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 507–518. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Brankovic, L., Fernau, H.: Combining Two Worlds: Parameterised Approximation for Vertex Cover. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010, Part I. LNCS, vol. 6506, pp. 390–402. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Chen, Y., Grohe, M., Grüber, M.: On Parameterized Approximability. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 109–120. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Cygan, M., Kowalik, Ł., Wykurz, M.: Exponential-time approximation of weighted set cover. Information Processing Letters 109, 957–961 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fernau, H.: Parameterized algorithmics for d-hitting set. International Journal of Computer Mathematics 87(14), 3157–3174 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fernau, H.: A top-down approach to search trees: Improved algorithmics for 3-hitting set. Algorithmica 57, 97–118 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fomin, F.V., Gaspers, S., Kratsch, D., Liedloff, M., Saurabh, S.: Iterative Compression and Exact Algorithms. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 335–346. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Kanj, I.A., Zhang, F.: 3-hitting set on Bounded Degree Hypergraphs: Upper and Lower Bounds on the Kernel Size. In: Marchetti-Spaccamela, A., Segal, M. (eds.) TAPAS 2011. LNCS, vol. 6595, pp. 163–174. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. Journal of Computer and System Sciences 74, 335–349 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32, 57–95 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wahlström, M.: Algorithms, Measures and Upper Bounds for Satisfiability and Related Problems. PhD thesis, Department of Computer and Information Science, Linköpings universitet, Sweden (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brankovic, L., Fernau, H. (2012). Parameterized Approximation Algorithms for Hitting Set . In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29116-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29115-9

  • Online ISBN: 978-3-642-29116-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics