On Parameterized Approximability

  • Yijia Chen
  • Martin Grohe
  • Magdalena Grüber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


Combining classical approximability questions with parameterized complexity, we introduce a theory of parameterized approximability. The main intention of this theory is to deal with the efficient approximation of small cost solutions for optimisation problems.


Approximation Algorithm Approximation Ratio Parameterized Problem Computable Function Propositional Formula 
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.
    Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterization of NP. Journal of the ACM 45(1), 70–122 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (2003)Google Scholar
  3. 3.
    Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: On the parameterized complexity of short computation and factorization. Archive for Mathematical Logic 36, 321–337 (1997)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cai, L., Huang, X.: Fixed-Parameter Approximation: Conceptual Framework and Approximability Results. These proceedingsGoogle Scholar
  5. 5.
    Cesati, M., Di Ianni, M.: Computation models for parameterized complexity. Mathematical Logic Quarterly 43, 179–202 (1997)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D., Kanj, I., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. In: Proceedings of the 19th IEEE Conference on Computational Complexity, pp. 150–160 (2004)Google Scholar
  7. 7.
    Courcelle, B., Engelfriet, J., Rozenberg, G.: Context-free handle-rewriting hypergraph grammars. In: Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Graph Grammars 1990. LNCS, vol. 532, pp. 253–268. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  8. 8.
    Dinur, I.: The PCP theorem by gap amplification. In: Proceedings of STOC 2006. 38th ACM Symposium on Theory of Computing, Seattle, Washington, USA (to appear, 2006)Google Scholar
  9. 9.
    Downey, R.G., Fellows, M.R.: Fixed-parameter tractability and completeness II: On completeness for W[1]. Journal of Theoretical Computer Science 141, 109–131 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  11. 11.
    Downey, R.G., Fellows, M.R., McCartin, C.: Parameterized Approximation Algorithms. These proceedingsGoogle Scholar
  12. 12.
    Even, G., Naor, J.S., Schieber, B., Sudan, M.: Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica 20(2), 151–174 (1998)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Fellows, M., Rosamond, F., Rotics, U., Szeider, S.: Clique-width minimization is NP-hard. In: Proceedings of STOC 2006. 38th ACM Symposium on Theory of Computing, Seattle, Washington, USA (to appear, 2006)Google Scholar
  14. 14.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  15. 15.
    Håstad, J.: Clique is hard to approximate within n 1 − ε. Electronic Colloquium on Computational Complexity, Report TR97-038 (1997)Google Scholar
  16. 16.
    Oum, S.: Approximating rank-width and clique-width quickly. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 49–58. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Oum, S., Seymour, P.: Approximating clique-width and branch-width. Journal of Combinatorial Theory, Series B (to appear)Google Scholar
  18. 18.
    Reed, B., Robertson, N., Seymour, P., Thomas, R.: Packing directed circuits. Combinatorica 16(4), 535–554 (1996)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Seymour, P.: Packing directed circuits fractionally. Combinatorica 15(2), 281–288 (1995)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Slivkins, A.: Parameterized tractability of edge-disjoint paths on directed acyclic graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 482–493. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yijia Chen
    • 1
  • Martin Grohe
    • 2
  • Magdalena Grüber
    • 2
  1. 1.BASICS, Department of Computer ScienceShanghai Jiaotong UniversityShanghaiChina
  2. 2.Institut für InformatikHumboldt-UniversitätBerlinGermany

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