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Towards Work-Efficient Parallel Parameterized Algorithms

  • Max Bannach
  • Malte SkambathEmail author
  • Till Tantau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)

Abstract

Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account that when we only have a small number of processors (between 2 and, say, 1024), it is more important that the parallel algorithms are work-efficient. In the present paper we investigate how work-efficient fpt algorithms can be designed. We review standard methods from fpt theory, like kernelization, search trees, and interleaving, and prove trade-offs for them between work efficiency and runtime improvements. This results in a toolbox for developing work-efficient parallel fpt algorithms.

Keywords

Parallel computation Fixed-parameter tractability Work efficiency 

References

  1. 1.
    Bannach, M., Stockhusen, C., Tantau, T.: Fast parallel fixed-parameter algorithms via color coding. In: IPEC 2015, pp. 224–235 (2015)Google Scholar
  2. 2.
    Bannach, M., Tantau, T.: Parallel multivariate meta-theorems. In: IPEC 2016, pp. 4:1–4:17 (2016)Google Scholar
  3. 3.
    Bannach, M., Tantau, T.: Computing hitting set kernels by AC\(^0\)-circuits. In: STACS 2018, pp. 9:1–9:14 (2018)Google Scholar
  4. 4.
    Bannach, M., Tantau, T.: Computing kernels in parallel: Lower and upper bounds. In: IPEC 2018, pp. 13:1–13:14 (2018)Google Scholar
  5. 5.
    Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: Advice classes of parameterized tractability. Ann. Pure Appl. Logic 84(1), 119–138 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cesati, M., Di Ianni, M.: Parameterized parallel complexity. In: Pritchard, D., Reeve, J. (eds.) Euro-Par 1998. LNCS, vol. 1470, pp. 892–896. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0057945CrossRefzbMATHGoogle Scholar
  7. 7.
    Cheetham, J., Dehne, F., Rau-Chaplin, A., Stege, U., Taillon, P.J.: Solving large fpt problems on coarse-grained parallel machines. JCSS 67(4), 691–706 (2003)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Chen, J., Kanj, I.A., Jia, W.: Vertex cover: further observations and further improvements. J. Algorithms 41(2), 280–301 (2001)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Downey, R., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999).  https://doi.org/10.1007/978-1-4612-0515-9CrossRefzbMATHGoogle Scholar
  10. 10.
    Elberfeld, M., Stockhusen, C., Tantau, T.: On the space and circuit complexity of parameterized problems: classes and completeness. Algorithmica 71(3), 661–701 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Han, Y.: An improvement on parallel computation of a maximal matching. IPL 56(6), 343–348 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    JáJá, J.: An Introduction to Parallel Algorithms. Addison-Wesley, Reading (1992)Google Scholar
  13. 13.
    Karp, R.M., Wigderson, A.: A fast parallel algorithm for the maximal independent set problem. J. ACM 32(4), 762–773 (1985)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter-tractable algorithms. IPL 73(3), 125–129 (2000)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceUniversität zu LübeckLübeckGermany
  2. 2.Department of Computer ScienceKiel UniversityKielGermany

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