Abstract
CP solvers predominantly use arc consistency (AC) as the default propagation method for binary constraints. Many stronger consistencies, such as triangle consistencies (e.g. RPC and maxRPC) exist, but their use is limited despite results showing that they outperform AC on many problems. This is due to the intricacies involved in incorporating them into solvers. On the other hand, singleton consistencies such as SAC can be easily crafted into solvers but they are too expensive in practice. Seeking a balance between the efficiency of triangle consistencies and the ease of implementation of singleton ones, we study the family of neighborhood singleton consistencies (NSCs) which extends the recently proposed neighborhood SAC (NSAC). We propose several new members of this family and study them both theoretically and experimentally. Our theroretical results show that the pruning power of the proposed NSCs ranges between that of RPC and (3,1)-consistency. Using a very simple algorithm for the implementation of NSCs, we demonstrate that certain members of the NSC family are quite competitive as general-purpose propagation methods for binary constraints, significantly outperforming the existing propagation techniques on some problem classes.
Similar content being viewed by others
Notes
SAC and NIC are incomparable [18].
References
Balafoutis, T., Paparrizou, A., Stergiou, K., Walsh, T. (2011). New algorithms for max restricted path consistency. Constraints, 16(4), 372–406.
Balafoutis, T., & Stergiou, K. (2008). Exploiting constraint weights for revision ordering in arc consistency algorithms. In ECAI-08 Workshop on modeling and solving problems with constraints.
Balafrej, A., Bessiere, C., Bouyakh, E., Trombettoni, G. (2014). Adaptive singleton-based consistencies. In Proceedings of the 28th AAAI conference on artificial intelligence (AAAI’14) (pp. 2601–2607).
Balafrej, A., Bessiere, C., Paparrizou, A. (2015). Multi-armed bandits for adaptive constraint propagation. In Proceedings of the twenty-fourth international joint conference on artificial intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015 (pp. 290–296).
Bartȧk, R., & Erben, R. (2004). A new algorithm for singleton arc consistency. In Proceedings of the seventeenth international Florida artificial intelligence (pp. 257–262).
Bennaceur, H., & Affane, M. (2001). Partition-k-AC: an efficient filtering technique combining domain partition and arc consistency. In 7th International conference on principles and practice of constraint programming - CP 2001 (pp. 560–564).
Berlandier, P. (1995). Improving domain filtering using restricted path consistency. In Proceedings of IEEE CAIA’95 (pp. 32–37).
Bessiere, C., Cardon, S., Debruyne, R., Lecoutre, C. (2011). Efficient algorithms for singleton arc consistency. Constraints, 16, 25–53.
Bessiere, C., & Debruyne, R. (2005). Optimal and suboptimal singleton arc consistency algorithms. In IJCAI-05, Proceedings of the nineteenth international joint conference on artificial intelligence, Edinburgh, Scotland, UK, July 30 - August 5, 2005 (pp. 54–59).
Bessiere, C., & Debruyne, R. (2008). Theoretical analysis of singleton arc consistency and its extensions. Artificial Intelligence, 172(1), 29–41.
Bessiere, C., Paparrizou, A., Stergiou, K. (2012). Strong bounds consistencies and their application to linear constraints. In Proceedings of AAAI’15 (pp. 3717–3723).
Bessiere, C., & Régin, J. C. (1996). MAC and combined heuristics: two reasons to forsake FC (and CBJ?) on hard problems. In Proceedings of CP’96 (pp. 61–75).
Bessiere, C., Stergiou, K., Walsh, T. (2008). Domain filtering consistencies for non-binary constraints. Artificial Intelligence, 172(6–7), 800–822.
Boussemart, F., Hemery, F., Lecoutre, C. (2004). Revision ordering heuristics for the constraint satisfaction problem. In CP’04 Workshop on constraint propagation and implementation. Toronto.
Boussemart, F., Heremy, F., Lecoutre, C., Sais, L. (2004). Boosting systematic search by weighting constraints. In Proceedings of ECAI’04 (pp. 482–486).
Carlier, J., & Pinson, E. (1994). Adjustment of heads and tails for the job-shop problem. European Journal of Operational Research, 78, 146–161.
Debruyne, R., & Bessiere, C. (1997). From restricted path consistency to max-restricted path consistency. In Proceedings of 3rd international conference on principles and practice of constraint programming (CP’97) (pp. 312–326).
Debruyne, R., & Bessiere, C. (2001). Domain filtering consistencies. Journal of Artificial Intelligence Research (JAIR), 14, 205–230.
Freeman, J.W. (1995). Improvements to propositional satisfiability search algorithms. PhD thesis, Computer and Information Science.
Freuder, E.C. (1985). A sufficient condition for backtrack-bounded search. JACM, 32(4), 755–761.
Freuder, E.C., & Elfe, C.D. (1996). Neighborhood inverse consistency preprocessing. In Proceedings of the 13th AAAI conference on artificial intelligence (AAAI’96) (pp. 202–208).
Geschwender, D., Karakashian, S., Woodward, R., Choueiry, B., Scott, S. Selecting the appropriate consistency algorithm for csps using machine learning classifiers.
Lecoutre, C., & Cardon, S. (2005). A greedy approach to establish singleton arc consistency. In IJCAI-05, proceedings of the nineteenth international joint conference on artificial intelligence, Edinburgh, Scotland, UK, July 30 - August 5, 2005 (pp. 199–204).
Lecoutre, C., & Hemery, F. (2007). A study of residual supports in arc consistency. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI’07) (pp. 125–130).
Lecoutre, C., Paparrizou, A., Stergiou, K. (2012). Extending STR to a higher-order consistency. In Proceedings of AAAI’13.
Likitvivatanavong, C., Wei, X., Yap, R.H.C. (2014). Higher-order consistencies through GAC on factor variables. In Principles and practice of constraint programming - 20th international conference, CP 2014. Proceedings (pp. 497–513).
Likitvivatanavong, C., Zhang, Y., Bowen, J., Shannon, S., Freuder, E.C. (2007). Arc consistency during search. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI’07) (pp. 137–142).
Martin, P., & Shmoys, D.B. (1996). A new approach to computing optimal schedules for the job-shop scheduling problem. In Proceedings of the 5th international conference on integer programming and combinatorial optimization, IPCO96 (pp. 389403).
Paparrizou, A., & Stergiou, K. (2012). Evaluating simple fully automated heuristics for adaptive constraint propagation. In IEEE 24th International conference on tools with artificial intelligence, ICTAI 2012, Athens, Greece, November 7-9, 2012 (pp. 880–885).
Paparrizou, A., & Stergiou, K. (2017). On neighborhood singleton consistencies. In Proceedings of the twenty-sixth international joint conference on artificial intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017 (pp. 736–742).
Prosser, P., Stergiou, K., Walsh, T. (2000). Singleton consistencies. In Proceedings of CP’00 (pp. 353–368).
Stergiou, K. (2008). Heuristics for dynamically adapting propagation. In Proceedings of ECAI’08 (pp. 485–489).
Stergiou, K. (2015). Restricted path consistency revisited. In Proceedings of the 21st international conference on principles and practice of constraint programming (CP’15) (pp. 419–428).
van Dongen, M.R.C. (2006). Beyond singleton arc consistency. In ECAI 2006, 17th European conference on artificial intelligence, 2006, proceedings (pp. 163–167).
Vion, J., & Debruyne, R. (2009). Light algorithms for maintaining max-RPC during search. In Proceedings of the 8th symposium on abstraction, reformulation and approximation (SARA’09) (pp. 167–174).
Wallace, R.J. (2015). SAC and neighbourhood SAC. AI Communications, 28(2), 345–364.
Wallace, R.J., & Neighbourhood, SAC. (2016). Extensions and new algorithms. AI Communications, 29(2), 249–268.
Wallace, R.J. (2016). Preprocessing versus search processing for constraint satisfaction problems. In Proceedings of RCRA’16 (pp. 89–103).
Wallace, R.J., & Freuder, E. (1992). Ordering heuristics for arc consistency algorithms. In AI/GI/VI (pp. 163–169). Vancouver.
Woodward, R., & Choueiry, B. (2017). Weight-based variable ordering in the context of high-level consistencies. arXiv:1711.00909.
Woodward, R., Choueiry, B., Bessiere, C. (2018). A reactive strategy for high-level consistency during search. In Proceedings of the twenty-seventh international joint conference on artificial intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden (pp. 1390–1397).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This is an extended version of paper [30] that appeared in the proceedings of IJCAI-2017.
Rights and permissions
About this article
Cite this article
Stergiou, K. Neighborhood singleton consistencies. Constraints 24, 94–131 (2019). https://doi.org/10.1007/s10601-018-9298-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10601-018-9298-1