Sequential Precede Chain for Value Symmetry Elimination

  • Graeme GangeEmail author
  • Peter J. Stuckey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)


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.



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


  1. 1.
    Law, Y.C., Lee, J.H.M.: Global constraints for integer and set value precedence. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 362–376. Springer, Heidelberg (2004). Scholar
  2. 2.
    Beldiceanu, N., Carlsson, M., Régin, J., Demassey, S.: Global constraint catalogue: \(\mathtt {int\_value\_precede\_chain}\). Accessed April 2018
  3. 3.
    Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004). Scholar
  4. 4.
    Cheng, K.C.K., Yap, R.H.C.: Maintaining generalized arc consistency on ad hoc r-ary constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 509–523. Springer, Heidelberg (2008). Scholar
  5. 5.
    Perez, G., Régin, J.-C.: Improving GAC-4 for table and MDD constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 606–621. Springer, Cham (2014). Scholar
  6. 6.
    Gange, G., Stuckey, P.J., Szymanek, R.: MDD propagators with explanation. Constraints 16(4), 407–429 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Katsirelos, G., Narodytska, N., Walsh, T.: Reformulating global grammar constraints. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 132–147. Springer, Heidelberg (2009). Scholar
  8. 8.
    Abío, I., Gange, G., Mayer-Eichberger, V., Stuckey, P.J.: On CNF encodings of decision diagrams. In: Quimper, C.-G. (ed.) CPAIOR 2016. LNCS, vol. 9676, pp. 1–17. Springer, Cham (2016). Scholar
  9. 9.
    Ohrimenko, O., Stuckey, P., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Freuder, E.C.: A sufficient condition for backtrack-free search. J. ACM 29(1), 24–32 (1982)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Chu, G.: Improving combinatorial optimization. Ph.D. thesis, Department of Computing and Information Systems, University of Melbourne (2011)Google Scholar
  12. 12.
    Law, Y.C., Lee, J.H.: Symmetry breaking constraints for value symmetries in constraint satisfaction. Constraints 11(2–3), 221–267 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Information TechnologyMonash UniversityMelbourneAustralia
  2. 2.Data61, CSIROMelbourneAustralia

Personalised recommendations