Abstract
Many computationally hard problems become tractable if the graph structure underlying the problem instance exhibits small treewidth. A recent approach to put this idea into practice is based on a declarative interface to specify dynamic programming over tree decompositions, delegating the computation to dedicated solvers. In this paper, we prove that this method can be applied to any problem whose fixed-parameter tractability follows from Courcelle’s Theorem.
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Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inf. Comput. 85(1), 12–75 (1990)
Langer, A., Reidl, F., Rossmanith, P., Sikdar, S.: Practical algorithms for MSO model-checking on tree-decomposable graphs (2013), http://tcs.rwth-aachen.de/~sikdar/index_files/article.pdf
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics And Its Applications. Oxford University Press (2006)
Flum, J., Frick, M., Grohe, M.: Query evaluation via tree-decompositions. J. ACM 49(6), 716–752 (2002)
Klarlund, N., Møller, A., Schwartzbach, M.I.: MONA implementation secrets. Int. J. Found. Comput. Sci. 13(4), 571–586 (2002)
Kneis, J., Langer, A., Rossmanith, P.: Courcelle’s theorem – a game-theoretic approach. Discrete Optimization 8(4), 568–594 (2011)
Langer, A., Reidl, F., Rossmanith, P., Sikdar, S.: Evaluation of an MSO-solver. In: Proc. ALENEX, pp. 55–63. SIAM / Omnipress (2012)
Courcelle, B., Durand, I.: Computations by fly-automata beyond monadic second-order logic. CoRR abs/1305.7120 (2013)
Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)
Bliem, B., Morak, M., Woltran, S.: D-FLAT: Declarative problem solving using tree decompositions and answer-set programming. TPLP 12(4-5), 445–464 (2012)
Langer, A., Rossmanith, P., Sikdar, S.: Linear-time algorithms for graphs of bounded rankwidth: A fresh look using game theory - (extended abstract). In: Ogihara, M., Tarui, J. (eds.) TAMC 2011. LNCS, vol. 6648, pp. 505–516. Springer, Heidelberg (2011)
Kloks, T.: Treewidth. LNCS, vol. 842. Springer, Heidelberg (1994)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Comput. 9(3/4), 365–386 (1991)
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., Thiele, S.: A user’s guide to gringo, clasp, clingo, and iclingo. Preliminary Draft (2010), http://potassco.sourceforge.net
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Answer Set Solving in Practice. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers (2012)
Frick, M., Grohe, M.: The complexity of first-order and monadic second-order logic revisited. Ann. Pure Appl. Logic 130(1-3), 3–31 (2004)
Gottlob, G., Pichler, R., Wei, F.: Monadic datalog over finite structures of bounded treewidth. ACM Trans. Comput. Log. 12(1) (2010)
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Bliem, B., Pichler, R., Woltran, S. (2013). Declarative Dynamic Programming as an Alternative Realization of Courcelle’s Theorem. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_4
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DOI: https://doi.org/10.1007/978-3-319-03898-8_4
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