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Breaking Symmetries with RootClique and LexTopSort

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Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

Bounded fractional hypertree width is the most general known structural property that guarantees polynomial-time solvability of the constraint satisfaction problem. Fichte et al. (CP 2018) presented a robust and scalable method for finding optimal fractional hypertree decompositions, based on an encoding to SAT Modulo Theory (SMT). In this paper, we provide an in-depth study of two powerful symmetry breaking predicates that allow us to further speed up the SMT-based decomposition: RootClique fixes the root of the decomposition tree; LexTopSort fixes the elimination ordering with respect to an underlying DAG. We perform an extensive empirical evaluation of both symmetry-breaking predicates with respect to the primal graph (which is known in advance) and the induced graph (which is generated during the search).

The work has been supported by the Austrian Science Fund (FWF), Grants Y698, 32441, and 32830, and the Vienna Science and Technology Fund, Grant WWTF ICT19-065. Hecher is also affiliated with the University of Potsdam, Germany.

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Notes

  1. 1.

    For comparability with frasmt, we used \(k=6\) (the option reported best  [16]).

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Author information

Authors and Affiliations

  1. School of Engineering Sciences, 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

    Stefan Szeider

Authors
  1. Johannes K. Fichte
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  2. Markus Hecher
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  3. Stefan Szeider
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Corresponding author

Correspondence to Johannes K. Fichte .

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Editors and Affiliations

  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Fichte, J.K., Hecher, M., Szeider, S. (2020). Breaking Symmetries with RootClique and LexTopSort. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_17

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_17

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