Abstract
The Balance constraint introduced by Beldiceanu ensures solutions are balanced. This is useful when, for example, there is a requirement for solutions to be fair. Balance bounds the difference B between the minimum and maximum number of occurrences of the values assigned to the variables. We show that achieving domain consistency on Balance is NP-hard. We therefore introduce a variant, AllBalance with a similar semantics that is only polynomial to propagate. We consider various forms of AllBalance and focus on AtMostallBalance which achieves what is usually the main goal, namely constraining the upper bound on B. We provide a specialized propagation algorithm, and a powerful decomposition both of which run in low polynomial time. Experimental results demonstrate the promise of these new filtering methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Networks Flows, Theory, Algorithms, and Applications. Prentice Hall (1993)
Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. Journal of the ACM (JACM) 56(2), 5 (2009)
Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Global Constraint Catalogue: Past, Present and Future. Constraints 12(1), 21–62 (2007)
Bessiere, C.: Constraint propagation. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. Elsevier (2006)
Cattafi, M., Herrero, R., Gavanelli, M., Nonato, M., Malucelli, F.: Improving Quality and Efficiency in Home Health Care: an application of Constraint Logic Programming for the Ferrara NHS unit. In: ICLP, pp. 415–424 (2012)
Hnich, B., Kiziltan, Z., Walsh, T.: Modelling a Balanced Academic Curriculum Problem. In: CPAIOR, pp. 121–131 (2002)
Lee, C., Loh, P.-S., Sudakov, B.: Bisections of graphs. Journal of Combinatorial Theory, Series B 103(5), 599–629 (2013)
Monette, J.-N., Schaus, P., Zampelli, S., Deville, Y., Dupont, P.: A CP Approach to the Balanced Academic Curriculum Problem. In: The Seventh International Workshop on Symmetry and Constraint Satisfaction Problems, Symcon 2007 (2007)
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)
Pesant, G., Régin, J.-C.: SPREAD: A Balancing Constraint Based on Statistics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 460–474. Springer, Heidelberg (2005)
Quimper, C.-G., Golynski, A., López-Ortiz, A., van Beek, P.: An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint. Constraints 10, 115–135 (2005)
Refalo, P.: Impact-Based Search Strategies for Constraint Programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004)
Régin, J.-C.: Generalized Arc Consistency for Global Cardinality Constraint. In: IAAI, pp. 209–215 (1996)
Schaus, P.: Solving Balancing and Bin-Packing problems with Constraint Programming. PhD thesis, Universite Catholique de Louvain (2009)
Schaus, P., Deville, Y., Dupont, P., Régin, J.-C.: Simplification and Extension of the SPREAD Constraint. In: Proc. of the 3rd Int’l Workshop on Constraint Propagation and Implementation, held alongside CP-06, pp. 77–91 (2006)
Schaus, P., Deville, Y., Dupont, P.E., Régin, J.-C.: The Deviation Constraint. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 260–274. Springer, Heidelberg (2007)
Schaus, P., Van Hentenryck, P., Régin, J.-C.: Scalable Load Balancing in Nurse to Patient Assignment Problems. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 248–262. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bessiere, C. et al. (2014). The Balance Constraint Family. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-10428-7_15
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10427-0
Online ISBN: 978-3-319-10428-7
eBook Packages: Computer ScienceComputer Science (R0)