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International Conference on Principles and Practice of Constraint Programming

CP 2018: Principles and Practice of Constraint Programming pp 109–127Cite as

An SMT Approach to Fractional Hypertree Width

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11008))

Abstract

Bounded fractional hypertree width () is the most general known structural property that guarantees polynomial-time solvability of the constraint satisfaction problem. Bounded generalizes other structural properties like bounded induced width and bounded hypertree width.

We propose, implement and test the first practical algorithm for computing the and its associated structural decomposition. We provide an extensive empirical evaluation of our method on a large class of benchmark instances which also provides a comparison with known exact decomposition methods for hypertree width. Our approach is based on an efficient encoding of the decomposition problem to SMT (SAT modulo Theory) with Linear Arithmetic as implemented in the SMT solver . The encoding is further strengthened by preprocessing and symmetry breaking methods. Our experiments show (i) that  can indeed be computed exactly for a wide range of benchmark instances, and (ii) that state-of-the art SMT techniques can be successfully applied for structural decomposition.

The work has been supported by the Austrian Science Fund (FWF), Grants Y698 and P26696, and the German Science Fund (DFG), Grant HO 1294/11-1. Fichte and Hecher are also affiliated with the University of Potsdam, Germany.

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Notes

  1. 1.

    See: github.com/daajoe/frasmt.

  2. 2.

    See: Benchmark repository [16] and results/raw data [17].

  3. 3.

    See: https://conda.io/docs/user-guide/install/download.html.

  4. 4.

    github.com/daajoe/detkdecomp.

  5. 5.

    https://www.dbai.tuwien.ac.at/proj/hypertree/benchmarks.zip.

  6. 6.

    See: spectreattack.com.

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Authors and Affiliations

  1. International Center of Computational Logic, TU Dresden, Dresden, Germany

    Johannes K. Fichte

  2. Database and Artificial Intelligence Group, TU Wien, Vienna, Austria

    Markus Hecher

  3. Algorithms and Complexity Group, TU Wien, Vienna, Austria

    Neha Lodha & Stefan Szeider

Authors
  1. Johannes K. Fichte
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  2. Markus Hecher
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  3. Neha Lodha
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  4. Stefan Szeider
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Corresponding authors

Correspondence to Johannes K. Fichte , Markus Hecher , Neha Lodha or Stefan Szeider .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John Hooker

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Fichte, J.K., Hecher, M., Lodha, N., Szeider, S. (2018). An SMT Approach to Fractional Hypertree Width. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-98334-9_8

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