Counting Maximal Independent Sets in Subcubic Graphs

  • Konstanty Junosza-Szaniawski
  • Michał Tuczyński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7147)

Abstract

The main result of this paper is an algorithm counting maximal independent sets in graphs with maximum degree at most 3 in time O *(1.2570 n ) and polynomial space.

Keywords

Maximum Degree Recursive Call Internal Vertex Primal Graph Sparse Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alber, J., Niedermeier, R.: Improved Tree Decomposition Based Algorithms for Domination-like Problems. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 613–628. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Dahllöf, V., Jonsson, P., Wahlström, M.: Couning models for 2SAT and 3SAT formulae. Theor. Comput. Sci. 332, 265–291 (2005)CrossRefMATHGoogle Scholar
  4. 4.
    Fomin, F.V., Kratsch, D.: Exact Exponential Algorithms. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  5. 5.
    Fomin, F.V., Hoie, K.: Pathwidth of cubic graphs and exact algorithms. Inf. Process. Lett. 97(5), 191–196 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Fürer, M., Kasiviswanathan, S.P.: Algorithms for Counting 2-Sat Solutions and Colorings with Applications. In: Kao, M.-Y., Li, X.-Y. (eds.) AAIM 2007. LNCS, vol. 4508, pp. 47–57. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Fomin, F.V., Gaspers, S., Saurabh, S., Stepanov, A.A.: On Two Techniques of Combining Branching and Treewidth. Algorithmica 54(2), 181–207 (2009)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gaspers, S., Kratsch, D., Liedloff, M.: On Independent Sets and Bicliques in Graphs. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds.) WG 2008. LNCS, vol. 5344, pp. 171–182. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Greenhill, C.: The complexity of counting colourings and independent sets in sparse graphs and hypergraphs. Comput. Complex 9, 52–73 (2000)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Jou, M.J., Chang, G.J.: Algorithmic aspects of counting independent sets. Ars. Comb. 65, 265–277 (2002)MathSciNetMATHGoogle Scholar
  11. 11.
    Junosza-Szaniawski, K., Tuczyński, M.: Counting maximal independent sets in subcubic graphs, Tech Rep., www.mini.pw.edu.pl/~szaniaws
  12. 12.
    Kullmann, O.: New methods for 3-SAT decision and worst-case analysis. Theor. Comput. Sci. 223(1-2), 1–72 (1999)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Kutzkov, K.: New upper bound for the #3-SAT problem. Inform. Process. Lett. 105, 1–5 (2007)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Lonc, Z., Truszczynski, M.: Computing minimal models, stable models and answer sets. Theory and Practice of Logic Prog. 6(4), 395–449 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Vadhan, S.P.: The Complexity of Counting in Sparse, Regular, and Planar Graphs. SIAM J. on Comput. 31, 398–427 (1997)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Wahlström, M.: A Tighter Bound for Counting Max-Weight Solutions to 2SAT Instances. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 202–213. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Konstanty Junosza-Szaniawski
    • 1
  • Michał Tuczyński
    • 1
  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

Personalised recommendations