Parameterized Complexity of Arc-Weighted Directed Steiner Problems

  • Jiong Guo
  • Rolf Niedermeier
  • Ondřej Suchý
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

We initiate a systematic parameterized complexity study of three fundamental network design problems on arc-weighted directed graphs: Directed Steiner Tree, Strongly Connected Steiner Subgraph, and Directed Steiner Network. We investigate their parameterized complexities with respect to the parameters “number of terminals”, “an upper bound on the size of the connecting network”, and the combination of both. We achieve several parameterized hardness as well as some fixed-parameter tractability results, in this way significantly extending previous results of Feldman and Ruhl [SIAM J. Comp. 2006].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arkin, E.M., Hassin, R., Shahar, S.: Increasing digraph arc-connectivity by arc addition, reversal and complement. Discrete Appl. Math. 122(1-3), 13–22 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On problems without polynomial kernels. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 563–574. Springer, Heidelberg (2008); Long version to appear in J. Comput. Syst. Sci.CrossRefGoogle Scholar
  3. 3.
    Ding, B., Yu, J.X., Wang, S., Qin, L., Zhang, X., Lin, X.: Finding top-k min-cost connected trees in databases. In: Proc. 23rd ICDE, pp. 836–845. IEEE, Los Alamitos (2007)Google Scholar
  4. 4.
    Dodis, Y., Khanna, S.: Design networks with bounded pairwise distance. In: Proc. 31th STOC, pp. 750–759. ACM, New York (1999)Google Scholar
  5. 5.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  6. 6.
    Dreyfus, S., Wagner, R.: The Steiner problem in graphs. Networks 1, 195–207 (1972)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Feldman, J., Ruhl, M.: The directed Steiner network problem is tractable for a constant number of terminals. SIAM J. Comput. 36(2), 543–561 (2006)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fellows, M.R., Hermelin, D., Rosamond, F.A., Vialette, S.: On the parameterized complexity of multiple-interval graph problems. Theor. Comput. Sci. 410(1), 53–61 (2009)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kortsarz, G., Nutov, Z.: Approximating minimum cost connectivity problems. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics. CRC, Boca Raton (2007)Google Scholar
  10. 10.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jiong Guo
    • 1
  • Rolf Niedermeier
    • 2
  • Ondřej Suchý
    • 3
  1. 1.Universität des SaarlandesSaarbrückenGermany
  2. 2.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  3. 3.Department of Applied Mathematics and Institute for Theoretical Computer ScienceCharles UniversityPrahaCzech Republic

Personalised recommendations