Improved Parameterized Algorithms for Weighted 3-Set Packing

  • Jianxin Wang
  • Qilong Feng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


Packing problems form an important class of NP-hard problems. For the weighted 3-Set Packing problem, we provide further theoretical study on the problem and present a deterministic algorithm of time O *(10.63k ). Based on the randomized divide-and-conquer method, the above result can be further reduced to O *(7.563k ), which significantly improves the previous best result O *(12.83k ).


Time Complexity Maximum Weight Packing Problem Splitting Function Claw Free Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alon, N., Yuster, R., Zwick, U.: Color-Coding. Journal of the ACM 42, 844–856 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arkin, E., Hassin, R.: Approximating Weighted Set Packing by Local Search. Math. Oper.Res. 24, 640–648 (1998)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bafna, V., Narayan, B., Ravi, R.: Nonoverlapping Local Alignments (Weighted Independent Sets of Axis-Parallel Rectangles). Discrete Appl. Math., 41–53 (1996)Google Scholar
  4. 4.
    Berman, P.: A d/2 Approximation for Maximum Weight Independent Set in d-claw Free Graphs. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 214–219. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Chandra, B., Halldorsson, M.M.: Greedy Local Improvement and Weighted Set Packing Approximation. Journal of Algorithms 39, 223–240 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chandra, B., Halldorsson, M.M.: Approximating Weighted Set Packing by Local Search. Journal of Algorithms, 223–240 (2001)Google Scholar
  7. 7.
    Chen, J., Lu, S.: Improved Parameterized Set Splitting Algorithms: a Probabilistic Approach. Algorithmica (to appear, 2008)Google Scholar
  8. 8.
    Chen, J., Lu, S., Zhang, F.: Improved Algorithms for Path, Matching, and Packing Problems. In: Proc. of SODA 2007, pp. 298–307 (2007)Google Scholar
  9. 9.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, New York (1999)Google Scholar
  10. 10.
    Fellows, M.R., Knauer, C., Nishimura, N., Ragde, P., Rosamond, F., Stege, U., Thilikos, D., Whitesides, S.: Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 311–322. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Liu, Y., Chen, J., Wang, J.: On Efficient FPT Algorithms for Weighted Matching and Packing Problems. In: Cai, J.-Y., Cooper, S.B., Zhu, H. (eds.) TAMC 2007. LNCS, vol. 4484, pp. 692–702. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Liu, Y., Lu, S., Chen, J., Sze, S.H.: Greedy Localization and Color-Coding: Improved Matching and Packing Algorithms. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 84–95. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Naor, M., Schulman, L., Srinivasan, A.: Splitters and Near-Optimal Derandomization. In: FOCS 1995, pp. 182–190 (1995)Google Scholar
  14. 14.
    Wang, J., Feng, Q.: An O *(3.523k) Parameterized Algorithm for 3-Set Packing. In: Proc. of TAMC 2008 (to appear, 2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jianxin Wang
    • 1
  • Qilong Feng
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaP.R. China

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