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Improved Parameterized Upper Bounds for Vertex Cover

  • Jianer Chen
  • Iyad A. Kanj
  • Ge Xia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)

Abstract

This paper presents an O(1.2738 k + kn)-time polynomial-space parameterized algorithm for Vertex Cover improving the previous O(1.286 k + kn)-time polynomial-space upper bound by Chen, Kanj, and Jia. The algorithm also improves the O(1.2745 k k 4 + kn)-time exponential-space upper bound for the problem by Chandran and Grandoni.

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References

  1. 1.
    Balasubramanian, R., Fellows, M., Raman, V.: An improved fixed parameter algorithm for Vertex Cover. Information Processing Letters 65, 163–168 (1998)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the Weighted Vertex Cover problem. Annals of Discrete Mathematics 25, 27–46 (1985)MathSciNetGoogle Scholar
  3. 3.
    Buss, J., Goldsmith, J.: Nondeterminism within P. SIAM Journal on Computing 22, 560–572 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cai, L., Juedes, D.: On the existence of subexponential parameterized algorithms. Journal of Computer and System Sciences 67(4), 789–807 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Sunil Chandran, L., Grandoni, F.: Refined memorisation for vertex cover. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 61–70. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Cheetham, J., Dehne, F., Rau-Chaplin, A., Stege, U., Taillon, P.: Solving large FPT problems on coarse grained parallel machines. Journal of Computer and System Sciences 67(4), 691–706 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chen, J., Kanj, I., Jia, W.: Vertex cover: further observations and further improvements. Journal of Algorithms 41, 280–301 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chen, J., Liu, L., Jia, W.: Improvement on Vertex Cover for low degree graphs. Networks 35, 253–259 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chlebik, M., Chlebikova, J.: Crown reductions for the minimum weighted vertex cover problem. Electronic Colloquium on Computational Complexity, Report No. 101 (2004)Google Scholar
  10. 10.
    Downey, R., Fellows, M.: Fixed-parameter tractability and completeness. Congressus Numerantium 87, 161–187 (1992)MathSciNetGoogle Scholar
  11. 11.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, New York (1999)Google Scholar
  12. 12.
    Ebengger, C., Hammer, P., de Werra, D.: Pseudo-boolean functions and stability of graphs. Annals of Discrete Mathematics 19, 83–98 (1984)Google Scholar
  13. 13.
    Fellows, M.R.: Blow-ups, win/Win’s, and crown rules: Some new directions in FPT. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 1–12. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  15. 15.
    Impagliazzo, R., Paturi, R.: Which problems have strongly exponential complexity? Journal of Computer and System Sciences 63, 512–530 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Nemhauser, G., Trotter, L.: Vertex packing: structural properties and algorithms. Mathematical Programming 8, 232–248 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Niedermeier, R., Rossmanith, P.: Upper bounds for Vertex Cover further improved. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 561–570. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Niedermeier, R., Rossmanith, P.: On efficient fixed-parameter algorithms for weighted vertex cover. Journal of Algorithms 47, 63–77 (2003)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Robson, J.M.: Algorithms for maximum independent set. Journal of Algorithms 6, 425–440 (1977)MathSciNetGoogle Scholar
  20. 20.
    Stege, U., Fellows, M.: An improved fixed-parameter-tractable algorithm for Vertex Cover. Technical Report 318, Department of Computer Science, ETH Zürich (April 1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jianer Chen
    • 1
  • Iyad A. Kanj
    • 2
  • Ge Xia
    • 3
  1. 1.Department of Computer ScienceTexas A&M UniversityCollege StationUSA
  2. 2.School of Computer Science, Telecommunications and Information SystemsDePaul UniversityChicagoUSA
  3. 3.Department of Computer ScienceLafayette CollegeEastonUSA

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