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Sequential Precede Chain for Value Symmetry Elimination

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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))

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Abstract

The main global constraint used for removing value symmetries is the value-precede-chain constraint which forces the first occurences of values in an ordered list to be appear in order. We introduce the seq-precede-chain constraint for the restricted, but common, case where the values are \(1,2, \ldots , k\), and variables in the constraint do not take values higher than k. We construct an efficient domain consistent propagator for this constraint, and show how we can generate explanations for its propagation. This leads us to an efficient domain consistent decomposition. We show how we can map any value-precede-chain to use instead seq-precede-chain. Experiments show that the new propagator and decomposition are better than existing approachs to propagating value-precede-chain.

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Notes

  1. 1.

    That is, \(\exists ~b_1,\ldots ,b_n.~((b_1 \leftrightarrow x_1=s) \wedge \bigwedge _{i= 2}^{n} b_i \leftrightarrow (b_{i-1} \vee \left\langle x_{i-1} = s \right\rangle ) \wedge \left\langle x_i = t \right\rangle \rightarrow b_{i-1}\). Here \(b_i\) records whether there is an occurrence of s no later than \(x_i\).

  2. 2.

    Note that the size equivalences are generated independently of other instance parameters, so may break existing dominance relationships.

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Acknowledgements

This research is supported by the Australian Research Council through grant DE160100568 and the Asian Office of Aerospace Research and Development grant 15-4016.

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Authors and Affiliations

  1. Faculty of Information Technology, Monash University, Melbourne, Australia

    Graeme Gange & Peter J. Stuckey

  2. Data61, CSIRO, Melbourne, Australia

    Peter J. Stuckey

Authors
  1. Graeme Gange
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  2. Peter J. Stuckey
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Correspondence to Graeme Gange .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John Hooker

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Gange, G., Stuckey, P.J. (2018). Sequential Precede Chain for Value Symmetry Elimination. 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_10

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  • DOI: https://doi.org/10.1007/978-3-319-98334-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-98333-2

  • Online ISBN: 978-3-319-98334-9

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