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Partitioning into Sets of Bounded Cardinality

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Parameterized and Exact Computation (IWPEC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5917))

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Abstract

We show that the partitions of an n-element set into k members of a given set family can be counted in time O((2 − ε)n), where ε> 0 depends only on the maximum size among the members of the family. Specifically, we give a simple combinatorial algorithm that counts the perfect matchings in a given graph on n vertices in time O(poly(n)ϕ n), where ϕ = 1.618... is the golden ratio; this improves a previous bound based on fast matrix multiplication.

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References

  1. Björklund, A., Husfeldt, T.: Exact algorithms for Exact Satisfiability and Number of Perfect Matchings. Algorithmica 52, 226–249 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion–exclusion. SIAM J. Comput., Special Issue for FOCS 2006 (to appear)

    Google Scholar 

  3. Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Fourier meets Möbius: fast subset convolution. In: 39th ACM Symposium on Theory of Computing (STOC 2007), pp. 67–74. ACM Press, New York (2007)

    Google Scholar 

  4. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9, 251–280 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. American Stat. Assoc. 58, 13–30 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  6. Valiant, L.G.: The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  7. Williams, R.: A new algorithm for optimal 2-constraint satisfaction and its implications. Theor. Comput. Sci. 348, 357–365 (2005)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, P.O.Box 68, FI-00014, Finland

    Mikko Koivisto

Authors
  1. Mikko Koivisto
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA

    Jianer Chen

  2. Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

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© 2009 Springer-Verlag Berlin Heidelberg

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Koivisto, M. (2009). Partitioning into Sets of Bounded Cardinality. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-11269-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11268-3

  • Online ISBN: 978-3-642-11269-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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