Multicut in Trees Viewed through the Eyes of Vertex Cover

  • Jianer Chen
  • Jia-Hao Fan
  • Iyad A. Kanj
  • Yang Liu
  • Fenghui Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

We take a new look at the multicut problem in trees through the eyes of the vertex cover problem. This connection, together with other techniques that we develop, allows us to significantly improve the O(k6) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k3). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O*(ρk), where \(\rho = (\sqrt{5} + 1)/2 \approx 1.618\). This improves the previous (time) upper bound of O*(2k), given by Guo and Niedermeier, for the problem.

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References

  1. 1.
    Abu-Khzam, F.A., Collins, R., Fellows, M., Langston, M., Suters, W., Symons, C.: Kernelization algorithms for the vertex cover problem: theory and experiments. In: Proceedings of ALENEX, pp. 62–69 (2004)Google Scholar
  2. 2.
    Bousquet, N., Daligault, J., Thomassé, S.: Multicut is fpt. In: CoRR, abs/1010.5197, 2010 (to appear in STOC 2011)Google Scholar
  3. 3.
    Bousquet, N., Daligault, J., Thomassé, S., Yeo, A.: A polynomial kernel for multicut in trees. In: Proceedings of STACS, pp. 183–194 (2009)Google Scholar
  4. 4.
    Buss, J., Goldsmith, J.: Nondeterminism within P. SIAM Journal on Computing 22, 560–572 (1993)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Costa, M., Letocart, L., Roupin, F.: Minimal multicut and maximal integer multiflow: A survey. European Journal of Operational Research 162(1), 55–69 (2005)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, New York (1999)CrossRefMATHGoogle Scholar
  7. 7.
    Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1), 3–20 (1997)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Guo, J., Niedermeier, R.: Fixed-parameter tractability and data reduction for multicut in trees. Networks 46(3), 124–135 (2005)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Marx, D.: Parameterized graph separation problems. Theoretical Computer Science 351(3), 394–406 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Marx, D., Razgon, I.: Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: CoRR, abs/1010.3633, 2010 (to appear in STOC 2011)Google Scholar
  11. 11.
    West, D.B.: Introduction to graph theory. Prentice Hall Inc., Upper Saddle River (1996)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jianer Chen
    • 1
  • Jia-Hao Fan
    • 1
  • Iyad A. Kanj
    • 2
  • Yang Liu
    • 3
  • Fenghui Zhang
    • 4
  1. 1.Department of Computer Science and EngineeringTexas A&M UniversityUSA
  2. 2.School of ComputingDePaul UniversityChicagoUSA
  3. 3.Department of Computer ScienceUniversity of Texas-Pan AmericanEdinburgUSA
  4. 4.Google KirklandKirklandUnited States

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