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International Conference on Principles and Practice of Constraint Programming

CP 2006: Principles and Practice of Constraint Programming - CP 2006 pp 499–513Cite as

Constraint Satisfaction with Bounded Treewidth Revisited

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

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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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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