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Constraint Satisfaction with Bounded Treewidth Revisited

  • Conference paper
Principles and Practice of Constraint Programming - CP 2006 (CP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4204))

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Abstract

The constraint satisfaction problem can be solved in polynomial time for instances where certain parameters (e.g., the treewidth of primal graphs) are bounded. However, there is a trade-off between generality and performance: larger bounds on the parameters yield worse time complexities. It is desirable to pay for more generality only by a constant factor in the running time, not by a larger degree of the polynomial. Algorithms with such a uniform polynomial time complexity are known as fixed-parameter algorithms.

In this paper we determine whether or not fixed-parameter algorithms for constraint satisfaction exist, considering all possible combinations of the following parameters: the treewidth of primal graphs, the treewidth of dual graphs, the treewidth of incidence graphs, the domain size, the maximum arity of constraints, and the maximum size of overlaps of constraint scopes. The negative cases are subject to the complexity theoretic assumption FPT ≠ W[1] which is the parameterized analog to P ≠ NP. For the positive cases we provide an effective fixed-parameter algorithm which is based on dynamic programming on “nice” tree decompositions.

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References

  1. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25(6), 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theoret. Comput. Sci. 209(1-2), 1–45 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bodlaender, H.L., Kloks, T.: Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms

    Google Scholar 

  4. Chen, H., Dalmau, V.: Beyond hypertree width: Decomposition methods without decompositions. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 167–181. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Cohen, D., Jeavons, P.: The complexity of constraint languages. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, vol. 8. Elsevier, Amsterdam (forthcoming, 2006)

    Google Scholar 

  6. Cohen, D., Jeavons, P., Gyssens, M.: A unified theory of structural tractability for constraint satisfaction and spread cut decomposition. In: Proc. IJCAI 2005, pp. 72–77 (2005)

    Google Scholar 

  7. Dechter, R.: Tractable structures for constraint satisfaction problems. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, part I, ch. 7. Elsevier, Amsterdam (forthcoming, 2006)

    Google Scholar 

  8. Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38(3), 353–366 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  10. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)

    Google Scholar 

  11. Freuder, E.C.: A sufficient condition for backtrack-bounded search. Journal of the ACM 32(4), 755–761 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ganzow, T., Gottlob, G., Musliu, N., Samer, M.: A CSP hypergraph library. Technical Report DBAI-TR-2005-50, Database and Artificial Intelligence Group, Vienna University of Technology (2005)

    Google Scholar 

  13. Gottlob, G., Grohe, M., Musliu, N., Samer, M., Scarcello, F.: Hypertree decompositions: Structure, algorithms, and applications. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 1–15. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions: a survey. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 37–57. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. J. of Computer and System Sciences 64(3), 579–627 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gottlob, G., Scarcello, F., Sideri, M.: Fixed-parameter complexity in AI and nonmonotonic reasoning. Artificial Intelligence 138(1-2), 55–86 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Grohe, M., Marx, D.: Constraint solving via fractional edge covers. In: Proc. SODA 2006, pp. 289–298. ACM, New York (2006)

    Chapter  Google Scholar 

  18. Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. J. of Computer and System Sciences 61(2), 302–332 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)

    Book  MATH  Google Scholar 

  20. Papadimitriou, C.H., Yannakakis, M.: On the complexity of database queries. J. of Computer and System Sciences 58(3), 407–427 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  21. Reed, B.: Finding approximate separators and computing tree width quickly. In: Proc. STOC 1992, pp. 221–228. ACM, New York (1992)

    Google Scholar 

  22. Szeider, S.: On fixed-parameter tractable parameterizations of SAT. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 188–202. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information Systems (DBAI), Vienna University of Technology, Austria

    Marko Samer

  2. Department of Computer Science, University of Durham, UK

    Stefan Szeider

Authors
  1. Marko Samer
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  2. Stefan Szeider
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Editor information

Editors and Affiliations

  1. LINA UMR CNRS 6241, University of Nantes,  

    Frédéric Benhamou

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© 2006 Springer-Verlag Berlin Heidelberg

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Samer, M., Szeider, S. (2006). Constraint Satisfaction with Bounded Treewidth Revisited. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_36

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  • DOI: https://doi.org/10.1007/11889205_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46267-5

  • Online ISBN: 978-3-540-46268-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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