Abstract
Exploiting solution counting information from individual constraints has led to some of the most efficient search heuristics in constraint programming. However, evaluating the number of solutions for the alldifferent constraint still presents a challenge: even though previous approaches based on sampling were extremely effective on hard instances, they are not competitive on easy to medium difficulty instances due to their significant computational overhead. In this paper we explore a new approach based on upper bounds, trading counting accuracy for a significant speedup of the procedure. Experimental results show a marked improvement on easy instances and even some improvement on hard instances. We believe that the proposed method is a crucial step to broaden the applicability of solution counting-based search heuristics.
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
Bregman, L.M.: Some Properties of Nonnegative Matrices and their Permanents. Soviet Mathematics Doklady 14(4), 945–949 (1973)
Gomes, C., Shmoys, D.: Completing Quasigroups or Latin Squares: A Structured Graph Coloring Problem. In: COLOR 2002: Proceedings of Computational Symposium on Graph Coloring and Generalizations, pp. 22–39 (2002)
Jurkat, W.B., Ryser, H.J.: Matrix Factorizations of Determinants and Permanents. Journal of Algebra 3, 1–27 (1966)
Liang, H., Bai, F.: An Upper Bound for the Permanent of (0,1)-Matrices. Linear Algebra and its Applications 377, 291–295 (2004)
Melo, R.A., Urrutia, S., Ribeiro, C.C.: The traveling tournament problem with predefined venues. Journal of Scheduling 12(6), 607–622 (2009)
Minc, H.: Upper Bounds for Permanents of (0, 1)-matrices. Bulletin of the American Mathematical Society 69, 789–791 (1963)
Pryor, J.: Branching Variable Direction Selection in Mixed Integer Programming. Master’s thesis, Carleton University (2009)
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.: A Filtering Algorithm for Constraints of Difference in CSPs. In: AAAI 1994: Proceedings of the Twelfth National Conference on Artificial Intelligence, vol. 1, pp. 362–367. American Association for Artificial Intelligence, Menlo Park (1994)
Soules, G.W.: New Permanental Upper Bounds for Nonnegative Matrices. Linear and Multilinear Algebra 51(4), 319–337 (2003)
Soules, G.W.: Permanental Bounds for Nonnegative Matrices via Decomposition. Linear Algebra and its Applications 394, 73–89 (2005)
Valiant, L.: The Complexity of Computing the Permanent. Theoretical Computer Science 8(2), 189–201 (1979)
Zanarini, A., Pesant, G.: Solution counting algorithms for constraint-centered search heuristics. Constraints 14(3), 392–413 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zanarini, A., Pesant, G. (2010). More Robust Counting-Based Search Heuristics with Alldifferent Constraints. In: Lodi, A., Milano, M., Toth, P. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2010. Lecture Notes in Computer Science, vol 6140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13520-0_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-13520-0_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13519-4
Online ISBN: 978-3-642-13520-0
eBook Packages: Computer ScienceComputer Science (R0)