Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Data Reduction for Domination in Graphs

  • Rolf Niedermeier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_99

Years and Authors of Summarized Original Work

  • 2004; Alber, Fellows, Niedermeier

Problem Definition


Dominating set Kernelization Reduction to a problem kernel 
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Recommended Reading

  1. 1.
    Alber J, Betzler N, Niedermeier R (2006) Experiments on data reduction for optimal domination in networks. Ann Oper Res 146(1):105–117MathSciNetzbMATHCrossRefGoogle Scholar
  2. 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):461–493MathSciNetzbMATHCrossRefGoogle Scholar
  3. 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 137–147Google Scholar
  4. 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):385–405Google Scholar
  5. 5.
    Alber J, Fellows MR, Niedermeier R (2004) Polynomial time data reduction for Dominating Set. J ACM 51(3):363–384MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Baker BS (1994) Approximation algorithms for NP-complete problems on planar graphs. J ACM 41(1):153–180MathSciNetzbMATHCrossRefGoogle Scholar
  7. 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):1077–1106MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Downey RG, Fellows MR (1999) Parameterized complexity. Springer, New YorkzbMATHCrossRefGoogle Scholar
  9. 9.
    Feige U (1998) A threshold of ln n for approximating set cover. J ACM 45(4):634–652MathSciNetzbMATHCrossRefGoogle Scholar
  10. 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 581–592Google Scholar
  11. 11.
    Guo J, Niedermeier R (2007) Invitation to data reduction and problemkernelization. ACM SIGACT News 38(1):31–45CrossRefGoogle Scholar
  12. 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 375–386Google Scholar
  13. 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 203–214Google Scholar
  14. 14.
    Haynes TW, Hedetniemi ST, Slater PJ (1998) Domination in graphs: advanced topics. Pure and applied mathematics, vol 209. Marcel Dekker, New YorkzbMATHGoogle Scholar
  15. 15.
    Haynes TW, Hedetniemi ST, Slater PJ (1998) Fundamentals of domination in graphs. Pure and applied mathematics, vol 208. Marcel Dekker, New YorkzbMATHGoogle Scholar
  16. 16.
    Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, New YorkzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Rolf Niedermeier
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of JenaJenaGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität BerlinBerlinGermany