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PW-CT: Extending Compact-Table to Enforce Pairwise Consistency on Table Constraints

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Principles and Practice of Constraint Programming (CP 2018)

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

Abstract

The Compact-Table (CT) algorithm is the current state-of-the-art algorithm for enforcing Generalized Arc Consistency (GAC) on table constraints during search. Recently, algorithms for enforcing Pairwise Consistency (PWC), which is strictly stronger than GAC, were shown to be advantageous for solving difficult problems. However, PWC algorithms can be costly in terms of CPU time and memory consumption. As a result, their overhead may offset the savings of search-space reduction. In this paper, we introduce PW-CT, an algorithm that modifies CT to enforce full PWC. We show that PW-CT avoids the high memory requirements of prior PWC algorithms and significantly reduces the time required to enforce PWC.

Supported by NSF Grant No. RI-1619344. Work completed utilizing the Holland Computing Center of the University of Nebraska, which receives support from the Nebraska Research Initiative. We thank the reviewers for constructive feedback.

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Change history

  • 22 September 2018

    The original version of the chapter was revised. The title has been corrected.

Notes

  1. 1.

    In this paper, we consider that a GAC algorithm applies tabular reduction.

  2. 2.

    64-bit on most current architectures.

  3. 3.

    Note that we have added the additional parameter \(c_i\) to supports[] to uniquely determine the constraint’s supports we are referring to in the pseudocode.

  4. 4.

    This can be done efficiently in C++ with Clang/GCC’s __builtin_popcountll.

  5. 5.

    http://www.cril.univ-artois.fr/CPAI08/.

  6. 6.

    Although dom/wdeg is generally more effective than dom/ddeg, the decisions made by dom/wdeg are considered too unstable to objectively allow comparing algorithms’ performance. Researchers studying the performance of HLC during search typically use dom/ddeg in their experiments [1, 20, 21].

  7. 7.

    Because bddLarge is an extreme outlier, we omit it from the results.

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Authors and Affiliations

  1. Constraint Systems Laboratory, University of Nebraska-Lincoln, Lincoln, USA

    Anthony Schneider & Berthe Y. Choueiry

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  1. Anthony Schneider
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  2. Berthe Y. Choueiry
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Correspondence to Anthony Schneider or Berthe Y. Choueiry .

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  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John Hooker

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Schneider, A., Choueiry, B.Y. (2018). PW-CT: Extending Compact-Table to Enforce Pairwise Consistency on Table Constraints. 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_23

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  • DOI: https://doi.org/10.1007/978-3-319-98334-9_23

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