Skip to main content
SpringerLink
Log in

Data Reduction for Domination in Graphs

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 92 Accesses

Years and Authors of Summarized Original Work

  • 2004; Alber, Fellows, Niedermeier

Problem Definition

Figure 1
figure 42 figure 42

The left-hand side shows the partitioning of the neighborhood of a single vertex v. The right-hand side shows the result of applying the presented data reduction rule to this particular (sub)graph

Full size image

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover 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

Recommended Reading

  1. Alber J, Betzler N, Niedermeier R (2006) Experiments on data reduction for optimal domination in networks. Ann Oper Res 146(1):105–117

    Article  MathSciNet  MATH  Google Scholar 

  2. Alber J, Bodlaender HL, Fernau H, Kloks T, Niedermeier R (2002) Fixed parameter algorithms for Dominating Set and related problems on planar graphs. Algorithmica 33(4):461–493

    Article  MathSciNet  MATH  Google Scholar 

  3. Alber J, Dorn B, Niedermeier R (2006) A general data reduction scheme for domination in graphs. In: Proceedings of 32nd SOFSEM. LNCS, vol 3831. Springer, Berlin, pp 137–147

    Google Scholar 

  4. Alber J, Fan H, Fellows MR, Fernau H, Niedermeier R, Rosamond F, Stege U (2005) A refined search tree technique for dominating Set on planar graphs. J Comput Syst Sci 71(4):385–405

    Google Scholar 

  5. Alber J, Fellows MR, Niedermeier R (2004) Polynomial time data reduction for Dominating Set. J ACM 51(3):363–384

    Article  MathSciNet  MATH  Google Scholar 

  6. Baker BS (1994) Approximation algorithms for NP-complete problems on planar graphs. J ACM 41(1):153–180

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen J, Fernau H, Kanj IA, Xia G (2007) Parametric duality and kernelization: lower bounds and upper bounds on kernel size. SIAM J Comput 37(4):1077–1106

    Article  MathSciNet  MATH  Google Scholar 

  8. Downey RG, Fellows MR (1999) Parameterized complexity. Springer, New York

    Book  MATH  Google Scholar 

  9. Feige U (1998) A threshold of ln n for approximating set cover. J ACM 45(4):634–652

    Article  MathSciNet  MATH  Google Scholar 

  10. Fomin FV, Thilikos DM (2004) Fast parameterized algorithms for graphs on surfaces: linear kernel and exponential speed-up. In: Proceedings of 31st ICALP. LNCS, vol 3142. Springer, Berlin, pp 581–592

    Google Scholar 

  11. Guo J, Niedermeier R (2007) Invitation to data reduction and problemkernelization. ACM SIGACT News 38(1):31–45

    Article  Google Scholar 

  12. Guo J, Niedermeier R (2007) Linear problem kernels for NPhard problems on planar graphs. In: Proceedings of 34th ICALP. LNCS, vol 4596. Springer, Berlin, pp 375–386

    Google Scholar 

  13. Guo J, Niedermeier R, Wernicke S (2006) Fixed-parameter tractability results for full-degree spanning tree and its dual. In: Proceedings of 2nd IWPEC. LNCS, vol 4196. Springer, Berlin, pp 203–214

    Google Scholar 

  14. Haynes TW, Hedetniemi ST, Slater PJ (1998) Domination in graphs: advanced topics. Pure and applied mathematics, vol 209. Marcel Dekker, New York

    MATH  Google Scholar 

  15. Haynes TW, Hedetniemi ST, Slater PJ (1998) Fundamentals of domination in graphs. Pure and applied mathematics, vol 208. Marcel Dekker, New York

    MATH  Google Scholar 

  16. Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, New York

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Jena, Jena, Germany

    Rolf Niedermeier

  2. Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Berlin, Germany

    Rolf Niedermeier

Authors
  1. Rolf Niedermeier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Niedermeier, R. (2016). Data Reduction for Domination in Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_99

Download citation

Publish with us

Policies and ethics

Search

Navigation