A General Data Reduction Scheme for Domination in Graphs

  • Jochen Alber
  • Britta Dorn
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3831)


Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity analysis in solving NP-hard problems. Its practical usefulness is confirmed by experimental work. Here, generalizing and extending previous work, we present a set of data reduction preprocessing rules on the way to compute optimal dominating sets in graphs. In this way, we arrive at the novel notion of “data reduction schemes.” In addition, we obtain data reduction results for domination in directed graphs that allow to prove a linear-size problem kernel for Directed Dominating Set in planar graphs.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization (1997)Google Scholar
  2. 2.
    Alber, J., Betzler, N., Niedermeier, R.: Experiments on Data Reduction for Optimal Domination in Networks. To appear, Annals of Operations Research (2005)Google Scholar
  3. 3.
    Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial Time Data Reduction for Dominating Set. Journal of the ACM 15(3), 363–384 (2004)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  5. 5.
    Chen, J., Fernau, H., Kanj, I.A., Xia, G.: Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 269–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Dorn, B.: Extended Data Reduction Rules for Domination in Graphs (in German). Student Project, WSI für Informatik, Universität Tübingen, Germany (2004)Google Scholar
  7. 7.
    Fomin, F.V., Thilikos, D.M.: Fast Parameterized Algorithms for Graphs on Surfaces: Linear Kernel and Exponential Speed-up. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 581–592. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jochen Alber
    • 1
  • Britta Dorn
    • 2
  • Rolf Niedermeier
    • 3
  1. 1.Power System Applications & ConsultingDIgSILENT GmbHGomaringenGermany
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations