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An FPT Algorithm for Set Splitting

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Graph-Theoretic Concepts in Computer Science (WG 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2880))

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Abstract

An FPT algorithm with a running time of O(n 4 + 2O(k) n 2.5) is described for the Set Splitting problem, parameterized by the number k of sets to be split. It is also shown that there can be no FPT algorithm for this problem with a running time of the form 2o(k) n c unless the satisfiability of n-variable 3SAT instances can be decided in time 2o(n).

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References

  1. Ageev, A.A., Sviridenko, M.I.: An approximation algorithm for hypergraph max k-cut with given sizes of parts. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 32–41. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Alber, J., Bodlaender, H.L., Fernau, H., Niedermeier, R.: Fixed parameter algorithms for planar dominating set and related problems. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 97–110. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Andersson, G., Engebretsen, L.: Better approximation algorithms and tighter analysis for set splitting and not-all-equal sat. In: ECCCTR: Electronic Colloquium on Computational Complexity (1997)

    Google Scholar 

  4. Arora, S., Karger, D., Karpinski, M.: Polynomial time approximation schemes for dense instances of NP-hard problems. In: Proc. ACM STOC, pp. 284–293 (1995)

    Google Scholar 

  5. Cai, L., Juedes, D.: Subexponential parameterized algorithms collapse the whierarchy. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, p. 273. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Cheetham, J., Dehne, F., Rau-Chaplin, A., Stege, U., Taillon, P.J.: Solving large FPT problems on coarse grained parallel machines. Journal of Computer and System Sciences (to appear)

    Google Scholar 

  7. Downey, R.D., Estivill-Castro, V., Fellows, M.R., Prieto-Rodriguez, E., Rosamond, F.A.: Cutting up is hard to do: The parameterized complexity of k-cut and related problems. In: Proc. Computing: The Australasian Theory Symposium (CATS 2003 ), Elsevier Electronic Notes in Computer Science, Adelaide (2003) (to appear)

    Google Scholar 

  8. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  9. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)

    MATH  Google Scholar 

  10. Hastad, J.: Some optimal inapproximability results. In: Proc. ACM STOC, pp. 1–10 (1997)

    Google Scholar 

  11. Hopkroft, J.E., Karp, R.M.: An n5/2 algorithm for maximum matching in bipartite graphs. SIAM J. Comput. 2, 225–231 (1973)

    Article  MathSciNet  Google Scholar 

  12. Kann, V., Lagergren, J., Panconesi, A.: Approximability of maximum splitting of k-sets and some other apx-complete problems. Information Processing Letters 58(3), 105–110 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lovasz, L.: Coverings and colorings of hypergraphs. In: Proc. 4th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, pp. 3–12 (1973)

    Google Scholar 

  14. Mehlhorn, K.: Data Structures And Algorithms. Springer, Heidelberg (1990)

    Google Scholar 

  15. Petrank, E.: The hardness of approximation: Gap location. Computational Complexity 4, 133–157 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang, H., Ling, C.X.: An improved learning algorithm for augmented naive Bayes. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS (LNAI), vol. 2035, pp. 581–586. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. Zwick, U.: Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint. In: Proc. SODA, pp. 201–220 (1998)

    Google Scholar 

  18. Zwick, U.: Outward rotations: A tool for rounding solutions of semidefinite programming relaxations, with applications to max cut and other problems. In: Proc. ACM STOC, pp. 679–687 (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Univ. of Newcastle, Australia

    Michael R. Fellows & Frances A. Rosamond

Authors
  1. Frank Dehne
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  2. Michael R. Fellows
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  3. Frances A. Rosamond
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

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© 2003 Springer-Verlag Berlin Heidelberg

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Dehne, F., Fellows, M.R., Rosamond, F.A. (2003). An FPT Algorithm for Set Splitting. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_16

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  • DOI: https://doi.org/10.1007/978-3-540-39890-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20452-7

  • Online ISBN: 978-3-540-39890-5

  • eBook Packages: Springer Book Archive

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