Advertisement

Answer Set Solving with Bounded Treewidth Revisited

  • Johannes K. Fichte
  • Markus Hecher
  • Michael Morak
  • Stefan Woltran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10377)

Abstract

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two kinds of graph representations of programs to exploit their treewidth as a parameter. Treewidth roughly measures to which extent the internal structure of a program resembles a tree. Our main contribution is the design of parameterized dynamic programming algorithms, which run in linear time if the treewidth and weights of the given program are bounded. Compared to previous work, our algorithms handle the full syntax of ASP. Finally, we report on an empirical evaluation that shows good runtime behaviour for benchmark instances of low treewidth, especially for counting answer sets.

Keywords

Parameterized algorithms Tree decompositions 

References

  1. 1.
    Abseher, M., Dusberger, F., Musliu, N., Woltran, S.: Improving the efficiency of dynamic programming on tree decompositions via machine learning. In: IJCAI 2015 (2015)Google Scholar
  2. 2.
    Bodlaender, H., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J. 51(3), 255–269 (2008)CrossRefGoogle Scholar
  3. 3.
    Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  4. 4.
    Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., Schaub, T.: ASP-core-2 input language format (2013)Google Scholar
  5. 5.
    Cygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer, Heidelberg (2015)CrossRefzbMATHGoogle Scholar
  6. 6.
    Eiter, T., Fink, M., Ianni, G., Krennwallner, T., Schüller, P.: Pushing efficient evaluation of HEX programs by modular decomposition. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 93–106. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-20895-9_10 CrossRefGoogle Scholar
  7. 7.
    Fichte, J.K., Szeider, S.: Backdoors to tractable answer-set programming. Artif. Intell. 220, 64–103 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Fichte, J.K., Hecher, M., Morak, M., Woltran, S.: Answer set solving with bounded treewidth revisited. CoRR, arXiv:1702.02890 (2017)
  9. 9.
    Jakl, M., Pichler, R., Woltran, S.: Answer-set programming with bounded treewidth. In: IJCAI 2009, vol. 2 (2009)Google Scholar
  10. 10.
    Pichler, R., Rümmele, S., Szeider, S., Woltran, S.: Tractable answer-set programming with weight constraints: bounded treewidth is not enough. Theory Pract. Log. Program. 14(2), 141–164 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Samer, M., Szeider, S.: Algorithms for propositional model counting. J. Discrete Algorithms 8(1), 50–64 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Sang, T., Bacchus, F., Beame, P., Kautz, H.A., Pitassi, T.: Combining component caching and clause learning for effective model counting. In: SAT 2004 (2004)Google Scholar
  13. 13.
    Syrjänen, T.: Lparse 1.0 user’s manual (2002). tcs.hut.fi/Software/smodels/lparse.ps
  14. 14.
    Thurley, M.: sharpSAT - counting models with advanced component caching and implicit BCP. In: SAT 2006 (2006)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Information SystemsWienAustria

Personalised recommendations