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On Parameterized Approximability

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Parameterized and Exact Computation (IWPEC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4169))

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Abstract

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.

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References

  1. Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterization of NP. Journal of the ACM 45(1), 70–122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (2003)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cai, L., Huang, X.: Fixed-Parameter Approximation: Conceptual Framework and Approximability Results. These proceedings

    Google Scholar 

  5. Cesati, M., Di Ianni, M.: Computation models for parameterized complexity. Mathematical Logic Quarterly 43, 179–202 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  10. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  11. Downey, R.G., Fellows, M.R., McCartin, C.: Parameterized Approximation Algorithms. These proceedings

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)

    Google Scholar 

  15. Håstad, J.: Clique is hard to approximate within n 1 − ε. Electronic Colloquium on Computational Complexity, Report TR97-038 (1997)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Oum, S., Seymour, P.: Approximating clique-width and branch-width. Journal of Combinatorial Theory, Series B (to appear)

    Google Scholar 

  18. Reed, B., Robertson, N., Seymour, P., Thomas, R.: Packing directed circuits. Combinatorica 16(4), 535–554 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  19. Seymour, P.: Packing directed circuits fractionally. Combinatorica 15(2), 281–288 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

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Chen, Y., Grohe, M., Grüber, M. (2006). On Parameterized Approximability. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_10

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  • DOI: https://doi.org/10.1007/11847250_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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