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A review of literature on parallel constraint solving

Published online by Cambridge University Press:  02 August 2018

IAN P. GENT ,
IAN MIGUEL ,
PETER NIGHTINGALE Open the ORCID record for PETER NIGHTINGALE [Opens in a new window] ,
CIARAN MCCREESH ,
PATRICK PROSSER ,
NEIL C. A. MOORE  and
CHRIS UNSWORTH
IAN P. GENT
Affiliation:
School of Computer Science, University of St Andrews, St Andrews KY16 9SX, UK (e-mail: ian.gent@st-andrews.ac.uk, ijm@st-andrews.ac.uk, pwn1@st-andrews.ac.uk)
IAN MIGUEL
Affiliation:
School of Computer Science, University of St Andrews, St Andrews KY16 9SX, UK (e-mail: ian.gent@st-andrews.ac.uk, ijm@st-andrews.ac.uk, pwn1@st-andrews.ac.uk)
PETER NIGHTINGALE
Affiliation:
School of Computer Science, University of St Andrews, St Andrews KY16 9SX, UK (e-mail: ian.gent@st-andrews.ac.uk, ijm@st-andrews.ac.uk, pwn1@st-andrews.ac.uk)
CIARAN MCCREESH
Affiliation:
School of Computing Science, University of Glasgow, Glasgow G12 8RZ, UK (e-mail: ciaran.mccreesh@glasgow.ac.uk, Patrick.Prosser@glasgow.ac.uk)
PATRICK PROSSER
Affiliation:
School of Computing Science, University of Glasgow, Glasgow G12 8RZ, UK (e-mail: ciaran.mccreesh@glasgow.ac.uk, Patrick.Prosser@glasgow.ac.uk)
NEIL C. A. MOORE
Affiliation:
Adobe Systems Incorporated, Edinburgh, UK (e-mail: nemoore@adobe.com)
CHRIS UNSWORTH
Affiliation:
School of Computing Science, University of Glasgow, Glasgow G12 8RZ, UK (e-mail: chris.unsworth79@gmail.com)
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Abstract

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As multi-core computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint algorithms are amenable to parallelisation; whether to use shared memory or distributed computation; whether to use static or dynamic decomposition; and how to best exploit portfolios and cooperating search. We review the literature, and see that we can sometimes do quite well, some of the time, on some instances, but we are far from a general solution. Yet there seems to be little overall guidance that can be given on how best to exploit multi-core computers to speed up constraint solving. We hope at least that this survey will provide useful pointers to future researchers wishing to correct this situation.

Keywords

Constraint programmingparallel computingpropositional satisfiabilityparallel search
Type
Survey Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 5-6: Special Issue on Parallel and Distributed Logic Programming , September 2018 , pp. 725 - 758
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

*We would like to thank EPSRC for funding this work through grants EP/E030394/1, EP/M003728/1, EP/P015638/1 and EP/P026842/1.

†This paper is a substantially revised and extended version of a paper that appeared in the PMCS 2011 Workshop on Parallel Methods for Constraint Solving (Gent et al. 2011).

References

Aigner, M., Biere, A., Kirsch, C. M., Niemetz, A. and Preiner, M. 2013. Analysis of portfolio-style parallel SAT solving on current multi-core architectures. In POS@ SAT. 28–40.Google Scholar
Akgün, Ö. 2014. Extensible Automated Constraint Modelling via Refinement of Abstract Problem Specifications. University of St Andrews.Google Scholar
Akgün, Ö., Frisch, A. M., Gent, I. P., Hussain, B. S., Jefferson, C., Kotthoff, L., Miguel, I. and Nightingale, P. 2013. Automated symmetry breaking and model selection in CONJURE. In International Conference on Principles and Practice of Constraint Programming. Springer, 107–116.Google Scholar
Akgün, Ö., Gent, I. P., Jefferson, C., Miguel, I. and Nightingale, P. 2014. Breaking conditional symmetry in automated constraint modelling with CONJURE. In Proc. of the Twenty-first European Conference on Artificial Intelligence. IOS Press, 3–8.Google Scholar
Akgün, Ö., Miguel, I. and Jefferson, C. 2010. Refining portfolios of constraint models with CONJURE. In Proc. of the 16th International Conference on Principles and Practice of Constraint Programming, Doctoral Programme Proceedings. 1–6.Google Scholar
Akgün, Ö., Miguel, I., Jefferson, C., Frisch, A. M. and Hnich, B. 2011. Extensible automated constraint modelling. In Proc. of the 25th AAAI Conference on Artificial Intelligence. AAAI Press, 4–11.Google Scholar
Amadini, R., Gabbrielli, M. and Mauro, J. 2015a. A multicore tool for constraint solving. In Proc. of the 24th International Joint Conference on Artificial Intelligence. 232–238.Google Scholar
Amadini, R., Gabbrielli, M. and Mauro, J. 2015b. SUNNY-CP: A sequential CP portfolio solver. In Proc. of the 30th Annual ACM Symposium on Applied Computing. ACM, 1861–1867.Google Scholar
Arbelaez, A. and Codognet, P. 2012. Massively parallel local search for SAT. In Proc. of the 24th IEEE International Conference on Tools with Artificial Intelligence. 57–64.Google Scholar
Arbelaez, A. and Codognet, P. 2013. From sequential to parallel local search for SAT. In Evolutionary Computation in Combinatorial Optimization. 157–168.Google Scholar
Arbelaez, A. and Codognet, P. 2014. A GPU implementation of parallel constraint-based local search. In Proc. of 22nd Euromicro International Conference on Parallel, Distributed and Network-Based Processing. IEEE, 648–655.Google Scholar
Arbelaez, A. and Hamadi, Y. 2011. Improving parallel local search for SAT. In Proc. of International Conference on Learning and Intelligent Optimization. 46–60.Google Scholar
Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.-M. and Piette, C. 2012. Revisiting clause exchange in parallel SAT solving. In Proc. of the 15th International Conference on Theory and Applications of Satisfiability Testing. 200–213.Google Scholar
Audemard, G. and Simon, L. 2014. Lazy clause exchange policy for parallel SAT solvers. In Proc. of the 17th International Conference on Theory and Applications of Satisfiability Testing. 197–205.Google Scholar
Bader, D. A., Hart, W. E. and Phillips, C. A. 2005. Parallel algorithm design for branch and bound. In Tutorials on Emerging Methodologies and Applications in Operations Research, vol. 76, Chap. 5, Harvey J. Greenberg, Ed. International Series in Operations Research & Management Science. Springer, New York, NY, USA, 1–44.Google Scholar
Balyo, T., Sanders, P. and Sinz, C. 2015. HordeSat: A massively parallel portfolio SAT solver. In Proc. of International Conference on Theory and Applications of Satisfiability Testing. 156–172.Google Scholar
Baudot, B. and Deville, Y. 1997. Analysis of distributed arc-consistency algorithms. Tech. Rep. RR-97-07, Université catholique de Louvain.Google Scholar
Bergman, D., Cire, A. A., Sabharwal, A., Samulowitz, H., Saraswat, V. and van Hoeve, W.-J. 2014. Parallel combinatorial optimization with decision diagrams. In Proc. of International Conference on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems. Springer, 351–367.Google Scholar
Biere, A. 2010. Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. Tech. Rep. 10/1, FMV Reports Series. Institute for Formal Models and Verification, Johannes Kepler University.Google Scholar
Biere, A. 2013. Lingeling, plingeling and treengeling entering the SAT competition 2013. In Proc. of SAT Competition 2013, Balint, A., Belov, A., Heule, M. and Järvisalo, M., Eds. Vol. B-2013-1 of Department of Computer Science Series of Publications B. University of Helsinki, 51–52.Google Scholar
Bordeaux, L., Hamadi, Y. and Samulowitz, H. 2009. Experiments with massively parallel constraint solving. In Proc. of the 21st International Joint Conference on Artificial Intelligence. 443–448.Google Scholar
Campeotto, F., Dal Palù, A., Dovier, A., Fioretto, F. and Pontelli, E. 2014a. Exploring the use of GPUs in constraint solving. In Proc. of the 16th International Symposium on Practical Aspects of Declarative Languages. 152–167.Google Scholar
Campeotto, F., Dovier, A., Fioretto, F. and Pontelli, E. 2014b. A GPU implementation of large neighborhood search for solving constraint optimization problems. In Proc. of the 21st European Conference on Artificial Intelligence. 189–194.Google Scholar
Caniou, Y., Codognet, P., Diaz, D. and Abreu, S. 2011. Experiments in parallel constraint-based local search. In Proc. of Evolutionary Computation in Combinatorial Optimization: 11th European Conference, Torino, Italy, April 27–29, 2011, 96–107.Google Scholar
Caniou, Y., Codognet, P., Richoux, F., Diaz, D. and Abreu, S. 2015. Large-scale parallelism for constraint-based local search: the costas array case study. Constraints 20, 1, 30–56.Google Scholar
Charnley, J., Colton, S. and Miguel, I. 2006. Automatic generation of implied constraints. In Proc. of the 17th European Conference on Artificial Intelligence. Vol. 141, 73–77.Google Scholar
Chrabakh, W. and Wolski, R. 2006. GridSAT: A system for solving satisfiability problems using a computational grid. Parallel Computing 32, 9, 660–687.Google Scholar
Chu, G., Schulte, C., and Stuckey, P. 2009. Confidence-based work stealing in parallel constraint programming. In Principles and Practices of Constraint Programming. Springer, 226–241.Google Scholar
Chu, G., Stuckey, P. J. and Harwood, A. 2008. PMiniSAT: A parallelization of MiniSAT 2.0. In SAT Race 2008.Google Scholar
Cire, A. A., Kadioglu, S. and Sellmann, M. 2014. Parallel restarted search. In Proc. of the 28th AAAI Conference on Artificial Intelligence, 842–848.Google Scholar
Clearwater, S. H., Huberman, B. A. and Hogg, T. 1991. Cooperative solution of constraint satisfaction problems. Science 254, 1181–1183.Google Scholar
Clocksin, W. 1987. Principles of the Delphi parallel inference machine. The Computer Journal 30, 5, 386–392.Google Scholar
Colton, S. and Miguel, I. 2001. Constraint generation via automated theory formation. In Proc. of the 7th International Conference on Principles and Practice of Constraint Programming. Springer, 575–579.Google Scholar
Crainic, T. G., Le Cun, B. and Roucairol, C. 2006. Parallel branch-and-bound algorithms. In Parallel Combinatorial Optimization. John Wiley & Sons, Hoboken, NJ, USA, 1–28.Google Scholar
Dal Palù, A., Dovier, A., Formisano, A. and Pontelli, E. 2015. CUD@SAT: SAT solving on GPUs. Journal of Experimental & Theoretical Artificial Intelligence 27, 293–316.Google Scholar
Davenport, A. J., Tsang, E. P. K., Wang, C. J. and Zhu, K. 1994. GENET: A connectionist architecture for solving constraint satisfaction problems by iterative improvement. In Proc. of the 12th National Conference on Artificial Intelligence. 325–330.Google Scholar
de Bruin, A., Kindervater, G. A. P. and Trienekens, H. W. J. M. 1995. Asynchronous parallel branch and bound and anomalies. In Proc. of 2nd International Workshop Parallel Algorithms for Irregularly Structured Problems, Lyon, France, Sep. 4–6, 1995, Ferreira, A. and Rolim, J. D. P., Eds. Lecture Notes in Computer Science, vol. 980. Springer, 363–377.Google Scholar
Diaz, D. 2001. Yet another local search method for constraint solving. In Proc. of Stochastic Algorithms: Foundations and Applications. Lecture Notes in Computer Science, vol. 2264, 73–90.Google Scholar
Diaz, D., Abreu, S. and Codognet, P. 2012. Targeting the cell broadband engine for constraint-based local search. Concurrency and Computation: Practice and Experience 24, 6, 647–660.Google Scholar
Dovier, A., Formisano, A., Pontelli, E. and Vella, F. 2016. A GPU implementation of the ASP computation. In Proc. of Practical Aspects of Declarative Languages – 18th International Symposium. 30–47.Google Scholar
Drakakis, K. 2006. A review of Costas arrays. Journal of Applied Mathematics 2006, 32.Google Scholar
Ehlers, T. and Stuckey, P. J. 2016. Parallelizing constraint programming with learning. In Proc. of Integration of AI and OR Techniques in Constraint Programming – 13th International Conference, Banff, AB, Canada, May 29–June 1, 2016, C. Quimper, Ed. Lecture Notes in Computer Science, vol. 9676. Springer, 142–158.Google Scholar
Faltings, B. 2006. Distributed constraint programming. In Handbook of Constraint Programming, Foundations of Artificial Intelligence, Rossi, Francesca, van Beek, Peter and Walsh, Toby, Eds., 699–729.Google Scholar
Fioretto, F., Le, T., Pontelli, E., Yeoh, W. and Son, T. C. 2015. Exploiting GPUs in solving (distributed) constraint optimization problems with dynamic programming. In Proc. of the 21st International Conference on Principles and Practice of Constraint Programming. 121–139.Google Scholar
Fioretto, F., Le, T., Yeoh, W., Pontelli, E. and Son, T. C. 2014. Improving DPOP with branch consistency for solving distributed constraint optimization problems. In Proc. of the 20th International Conference on Principles and Practice of Constraint Programming. 307–323.Google Scholar
Fioretto, F., Yeoh, W. and Pontelli, E. 2016. A dynamic programming-based MCMC framework for solving DCOPs with GPUs. In Proc. of the 22nd International Conference on Principles and Practice of Constraint Programming. 813–831.Google Scholar
Fischetti, M., Monaci, M. and Salvagnin, D. 2014. Self-splitting of workload in parallel computation. In Proc. of Integration of AI and OR Techniques in Constraint Programming – 11th International Conference, Cork, Ireland, May 19–23, 2014, Simonis, H., Ed. Lecture Notes in Computer Science, vol. 8451. Springer, 394–404>..>Google Scholar
Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Pearson, J. and Walsh, T. 2001. Symmetry in matrix models. In Proc. of SymCon'01, the 1st International Workshop on Symmetry in CSPs.Google Scholar
Flener, P., Frisch, A. M., Hnich, B., Kiziltan, Z., Miguel, I. and Walsh, T. 2002. Matrix modelling: Exploiting common patterns in constraint programming. In Proc. of the International Workshop on Reformulating Constraint Satisfaction Problems. 27–41.Google Scholar
Freuder, E. C. 1982. A sufficient condition for backtrack-free search. Journal of the ACM 29, 1, 24–32.Google Scholar
Frisch, A. M., Grum, M., Jefferson, C., Hernández, B. M. and Miguel, I. 2005. The essence of Essence: A constraint language for specifying combinatorial problems. In Proc. of the 4th International Workshop on Modelling and Reformulating Constraint Satisfaction Problems. 73–88.Google Scholar
Frisch, A. M., Grum, M., Jefferson, C., Hernández, B. M. and Miguel, I. 2007a. The design of Essence: A constraint language for specifying combinatorial problems. In Proc. of the 20th International Joint Conference on Artificial Intelligence. 80–87.Google Scholar
Frisch, A. M., Harvey, W., Jefferson, C., Hernández, B. M. and Miguel, I. 2008. Essence: A constraint language for specifying combinatorial problems. Constraints 13, 3, 268–306.Google Scholar
Frisch, A. M., Jefferson, C., Hernández, B. M. and Miguel, I. 2007b. Symmetry in the generation of constraint models. In Proc. of the International Symmetry Conference.Google Scholar
Frisch, A. M., Jefferson, C. and Miguel, I. 2004. Symmetry breaking as a prelude to implied constraints: A constraint modelling pattern. In Proc. of the 16th European Conference on Artificial Intelligence. 171–175.Google Scholar
Frühwirth, T. W., Michel, L. and Schulte, C. 2006. Constraints in procedural and concurrent languages. In Handbook of Constraint Programming, Foundations of Artificial Intelligence, Rossi, Francesca, van Beek, Peter, Walsh, Toby, Eds., 453–494.Google Scholar
Furukawa, K. and Ueda, K. 1988. GHC – A language for a new age of parallel programming. In Proc. of Foundations of Software Technology and Theoretical Computer Science, 8th Conference, Pune, India, December 21–23, 1988, Nori, K. V. and Kumar, S., Eds. Lecture Notes in Computer Science, vol. 338. Springer, 364–376.Google Scholar
Garcia, V., Debreuve, E. and Barlaud, M. 2008. Fast k nearest neighbor search using GPU. In Proc. of 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops. 1–6.Google Scholar
Gecode Team. 2006. Gecode: Generic constraint development environment. URL: http://www.gecode.orgGoogle Scholar
Gent, I. P., Jefferson, C., Miguel, I., Moore, N. C. A., Nightingale, P., Prosser, P. and Unsworth, C. 2011. A preliminary review of literature on parallel constraint solving. In Proc. of PMCS 2011 Workshop on Parallel Methods for Constraint Solving. 499–504.Google Scholar
Gent, I. P., Miguel, I. and Rendl, A. 2008. Common subexpression elimination in automated constraint modelling. In Proc. of the International Workshop on Modeling and Solving Problems with Constraints. 24–30.Google Scholar
Gharbi, N. 2015. Using parallel singleton arc consistency to enhance constraint solving. In Proc. of the 27th IEEE International Conference on Tools with Artificial Intelligence. 17–24.Google Scholar
Gomes, C. P. and Selman, B. 2001. Algorithm portfolios. Artificial Intelligence 126, 1/2, 43–62.Google Scholar
Granvilliers, L. and Hains, G. 2000. A conservative scheme for parallel interval narrowing. Information Processing Letters 74, 3/4, 141–146.Google Scholar
Grinshpoun, T., Grubshtein, A., Zivan, R., Netzer, A. and Meisels, A. 2013. Asymmetric distributed constraint optimization problems. Journal of Artificial Intelligence Research 47, 613–647.Google Scholar
Guo, L., Hamadi, Y., Jabbour, S. and Sais, L. 2010. Diversification and intensification in parallel SAT solving. In Proc. of 16th International Conference on Principles and Practice of Constraint Programming. 252–265.Google Scholar
Gustafson, J. L. 1988. Reevaluating Amdahl's law. Communications of the ACM 31, 5, 532–533.Google Scholar
Hamadi, Y. 2002. Optimal distributed arc-consistency. Constraints 7, 3/4, 367–385.Google Scholar
Hamadi, Y., Jabbour, S., Piette, C. and Sais, L. 2011. Deterministic parallel DPLL. Journal on Satisfiability, Boolean Modeling and Computation 7, 4, 127–132.Google Scholar
Hamadi, Y., Jabbour, S. and Sais, L. 2009a. Control-based clause sharing in parallel SAT solving. In Proc. of 21st International Joint Conference on Artificial Intelligence. 499–504.Google Scholar
Hamadi, Y., Jabbour, S. and Sais, L. 2009b. ManySAT: A parallel SAT solver. Journal on Satisfiability, Boolean Modeling and Computation 6, 245–262.Google Scholar
Hamadi, Y. and Wintersteiger, C. 2013. Seven challenges in parallel SAT solving. AI Magazine 34, 2, 99–106.Google Scholar
Held, J., Bautista, J. and Koehl, S. 2006. From a Few Cores to Many: A Tera-Scale Computing Research Overview. Intel White Paper.Google Scholar
Henz, M., Smolka, G. and Würtz, J. 1993. Oz – A programming language for multi-agent systems. In Proc. of the 13th International Joint Conference on Artificial Intelligence, Chambéry, France, August 28–September 3, 1993, R. Bajcsy, Ed. Morgan Kaufmann, 404–409.Google Scholar
Heule, M. J., Kullmann, O., Wieringa, S. and Biere, A. 2011. Cube and conquer: Guiding CDCL SAT solvers by lookaheads. In Haifa Verification Conference. Springer, 50–65.Google Scholar
Heule, M. J. H. and Kullmann, O. 2017. The science of brute force. Communications of the ACM 60, 70–79.Google Scholar
Heule, M. J. H., Kullmann, O. and Marek, V. W. 2016. Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In Proc. of the 19th International Conference on Theory and Applications of Satisfiability Testing. 228–245.Google Scholar
Hirayama, K. and Yokoo, M. 2005. The distributed breakout algorithms. Artificial Intelligence 161, 1/2, 89–115.Google Scholar
Hölldobler, S., Manthey, N., Nguyen, V. H., Stecklina, J. and Steinke, P. 2011. A short overview on modern parallel SAT-solvers. In Proc. of International Conference on Advanced Computer Science and Information Systems. 201–206.Google Scholar
Hoos, H., Kaminski, R., Lindauer, M. and Schaub, T. 2015. aspeed: Solver scheduling via answer set programming. Theory and Practice of Logic Programming 15, 1, 117–142.Google Scholar
Huberman, B. A., Lukose, R. M. and Hogg, T. 1997. An economics approach to hard computational problems. Science 275, 5296, 51–54.Google Scholar
Hurley, B., Kotthoff, L., Malitsky, Y. and O'Sullivan, B. 2014. Proteus: A hierarchical portfolio of solvers and transformations. In Proc. of International Conference on AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer International Publishing, 301–317.Google Scholar
Hyvärinen, A., Junttila, T. and Niemelä, I. 2009. Incorporating clause learning in grid-based randomized SAT solving. Journal on Satisfiability, Boolean Modeling and Computation 6, 223–244.Google Scholar
Hyvärinen, A. E. J. and Manthey, N. 2012. Designing scalable parallel SAT solvers. In Theory and Applications of Satisfiability Testing – SAT 2012, Cimatti, A. and Sebastiani, R., Eds. Springer, Berlin, Heidelberg, 214–227.Google Scholar
Jaffar, J., Santosa, A. E., Yap, R. H. C. and Zhu, K. Q. 2004. Scalable distributed depth-first search with greedy work stealing. In Proc. of 16th IEEE International Conference on Tools with Artificial Intelligence. 98–103.Google Scholar
Järvisalo, M., Heule, M. and Biere, A. 2012. Inprocessing rules. In Proc. of the 6th International Joint Conference on Automated Reasoning. 355–370.Google Scholar
Kadioglu, S., Malitsky, Y., Sabharwal, A., Samulowitz, H. and Sellmann, M. 2011. Algorithm selection and scheduling. In Proc. of International Conference on Principles and Practice of Constraint Programming. Springer, 454–469.Google Scholar
Karp, R. M. and Zhang, Y. 1993. Randomized parallel algorithms for backtrack search and branch-and-bound computation. Journal of the ACM 40, 765–789.Google Scholar
Kasif, S. 1990. On the parallel complexity of discrete relaxation in constraint satisfaction networks. Artificial Intelligence 45, 3, 275–286.Google Scholar
Kasif, S. and Delcher, A. L. 1994. Local consistency in parallel constraint satisfaction networks. Artificial Intelligence 69, 1/2, 307–327.Google Scholar
Katsirelos, G., Sabharwal, A., Samulowitz, H. and Simon, L. 2013. Resolution and parallelizability: Barriers to the efficient parallelization of SAT solvers. In Proc. of the 27th AAAI Conference on Artificial Intelligence. 481–488.Google Scholar
Kirousis, L. M. 1993. Fast parallel constraint satisfaction. Artificial Intelligence 64, 1, 147–160.Google Scholar
Kotthoff, L. 2014. Algorithm selection for combinatorial search problems: A survey. AI Magazine 35, 3, 48–60.Google Scholar
Kotthoff, L. and Moore, N. C. A. 2010. Distributed solving through model splitting. In Proc. of 3rd Workshop on Techniques for Implementing Constraint Programming Systems.Google Scholar
Lai, T. and Sahni, S. 1984. Anomalies in parallel branch-and-bound algorithms. Communications of the ACM 27, 6, 594–602.Google Scholar
Léauté, T., Ottens, B. and Szymanek, R. 2009. FRODO 2.0: An open-source framework for distributed constraint optimization. In Proc. of the IJCAI'09 Distributed Constraint Reasoning Workshop, Pasadena, California, USA, 160–164. URL: https://frodo-ai.techGoogle Scholar
Li, G. and Wah, B. W. 1986. Coping with anomalies in parallel branch-and-bound algorithms. IEEE Transactions on Computers 35, 6, 568–573.Google Scholar
Lindauer, M., Hoos, H. and Hutter, F. 2015. From sequential algorithm selection to parallel portfolio selection. In International Conference on Learning and Intelligent Optimization. Springer, 1–16.Google Scholar
Lindauer, M., Hoos, H., Leyton-Brown, K. and Schaub, T. 2017. Automatic construction of parallel portfolios via algorithm configuration. Artificial Intelligence 244, 272–290.Google Scholar
Machado, R., Pedro, V. and Abreu, S. 2013. On the scalability of constraint programming on hierarchical multiprocessor systems. In Proc. of 42nd International Conference on Parallel Processing, ICPP 2013, Lyon, France, October 1–4, 2013. IEEE Computer Society, 530–535.Google Scholar
Maher, M. J. 1987. Logic semantics for a class of committed-choice programs. In Proc. of the 4th International Conference on Logic Programming, Melbourne, Victoria, Australia, May 25–29, 1987, J. Lassez, Ed. MIT Press, 858–876.Google Scholar
Malapert, A., Régin, J.-C. and Rezgui, M. 2016. Embarrassingly parallel search in constraint programming. Journal of Artificial Intelligence Research 57, 421–464.Google Scholar
Malitsky, Y., Sabharwal, A., Samulowitz, H. and Sellmann, M. 2012. Parallel SAT solver selection and scheduling. In Proc. of the 18th International Conference on Principles and Practice of Constraint Programming. Springer, 512–526.Google Scholar
Malitsky, Y., Sabharwal, A., Samulowitz, H. and Sellmann, M. 2013a. Algorithm portfolios based on cost-sensitive hierarchical clustering. In Proc. of the 23rd International Joint Conference on Artificial Intelligence. 608–614.Google Scholar
Malitsky, Y., Sabharwal, A., Samulowitz, H. and Sellmann, M. 2013b. Parallel Lingeling, CCASat, and CSCH-based portfolios. In Proc. of the SAT Competition 2013. 26–27.Google Scholar
Manolios, P. and Zhang, Y. 2006. Implementing survey propagation on graphics processing units. In Proc. of Theory and Applications of Satisfiability Testing – SAT 2006. Lecture Notes in Computer Science. vol. 4121. 311–324.Google Scholar
Manthey, N. 2011a. A More Efficient Parallel Unit Propagation, Tech. Rep. 11-04, Knowledge Representation and Reasoning. Technische Universität Dresden.Google Scholar
Manthey, N. 2011b. Parallel sat solving – using more cores. In Proc. of Pragmatics of SAT Workshop.Google Scholar
Martins, R., Manquinho, V. and Lynce, I. 2012. An overview of parallel SAT solving. Constraints 17, 304–347.Google Scholar
McCreesh, C. and Prosser, P. 2015. The shape of the search tree for the maximum clique problem and the implications for parallel branch and bound. ACM Transactions on Parallel Computing 2, 1, 8:1–8:27.Google Scholar
Menouer, T., Rezgui, M., Cun, B. L. and Régin, J. 2016. Mixing static and dynamic partitioning to parallelize a constraint programming solver. International Journal of Parallel Programming 44, 3, 486–505.Google Scholar
Michel, L., See, A. and Van Hentenryck, P. 2006. Distributed constraint-based local search. In Proc. of Principles and Practice of Constraint Programming – CP 2006. 344–356.Google Scholar
Michel, L., See, A. and Van Hentenryck, P. 2007. Parallelizing constraint programs transparently. In Proc. of Principles and Practice of Constraint Programming – CP 2007. 514–528.Google Scholar
Michel, L., See, A. and Van Hentenryck, P. 2009. Parallel and distributed local search in COMET. Computers & Operations Research 36, 2357–2375.Google Scholar
Moisan, T., Gaudreault, J. and Quimper, C.-G. 2013. Parallel discrepancy-based search. In Proc. of the 19th International Conference on Principles and Practice of Constraint Programming. 30–46.Google Scholar
Moisan, T., Quimper, C.-G. and Gaudreault, J. 2014. Parallel depth-bounded discrepancy search. In Proc. of International Conference on AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer, 377–393.Google Scholar
Montelius, J. and Ali, K. A. M. 1996. An and/or-parallel implementation of AKL. New Generation Computing 14, 1, 31–52.Google Scholar
Munawar, A., Wahib, M., Munetomo, M. and Akama, K. 2009. Hybrid of genetic algorithm and local search to solve MAX-SAT problem using nVidia CUDA framework. Genetic Programming and Evolvable Machines 10, 391–415.Google Scholar
Munera, D., Diaz, D. and Abreu, S. 2014. Towards parallel constraint-based local search with the X10 language. In Declarative Programming and Knowledge Management: Declarative Programming Days, KDPD 2013, Unifying INAP, WFLP, and WLP, Kiel, Germany, September 11–13, 2013, Revised Selected Papers, Hanus, M. and Rocha, R., Eds. Springer International Publishing, 169–184.Google Scholar
Munera, D., Diaz, D., Abreu, S. and Codognet, P. 2014. A parametric framework for cooperative parallel local search. In Evolutionary Computation in Combinatorial Optimisation: 14th European Conference, EvoCOP 2014, Granada, Spain, April 23-25, 2014, Revised Selected Papers, Blum, C. and Ochoa, G., Eds. Springer, Berlin, Heidelberg, 13–24.Google Scholar
Munera, D., Diaz, D., Abreu, S., Rossi, F., Saraswat, V. A. and Codognet, P. 2015. Solving hard stable matching problems via local search and cooperative parallelization. In Proc. of the 29th AAAI Conference on Artificial Intelligence. 1212–1218.Google Scholar
Netzer, A., Meisels, A. and Zivan, R. 2016. Distributed envy minimization for resource allocation. Autonomous Agents and Multi-Agent Systems 30, 2, 364–402.Google Scholar
Nguyen, T. and Deville, Y. 1995. A distributed arc-consistency algorithm. In Proc. of 1st International Workshop on Concurrent Constraint Satisfaction.Google Scholar
Nguyen, T. and Deville, Y. 1998. A distributed arc-consistency algorithm. Science of Computer Programming 30, 227–250.Google Scholar
Nightingale, P., Akgün, Ö., Gent, I. P., Jefferson, C. and Miguel, I. 2014. Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination. In Proc. of International Conference on Principles and Practice of Constraint Programming. Springer, 590–605.Google Scholar
Nightingale, P., Akgün, O., Gent, I. P., Jefferson, C., Miguel, I. and Spracklen, P. 2017. Automatically improving constraint models in Savile Row. Artificial Intelligence 251, 35–61.Google Scholar
Nightingale, P., Spracklen, P. and Miguel, I. 2015. Automatically improving SAT encoding of constraint problems through common subexpression elimination in Savile Row. In International Conference on Principles and Practice of Constraint Programming. Springer, 330–340.Google Scholar
O'Mahony, E., Hebrard, E., Holland, A., Nugent, C. and O'Sullivan, B. 2008. Using case-based reasoning in an algorithm portfolio for constraint solving. In Proc. of Irish Conference on Artificial Intelligence and Cognitive Science, 210–216.Google Scholar
Otten, L. and Dechter, R. 2017. AND/OR branch-and-bound on a computational grid. Journal of Artificial Intelligence Research 59, 351–435.Google Scholar
Palmieri, A., Régin, J. and Schaus, P. 2016. Parallel strategies selection. In Proc. 22nd International Conference on Principles and Practice of Constraint Programming. 388–404.Google Scholar
Perron, L. 1999. Search procedures and parallelism in constraint programming. In Proc. of International Conference on Principles and Practice of Constraint Programming, 346–361.Google Scholar
Prosser, P., Conway, C. and Muller, C. 1992. A constraint maintenance system for the distributed resource allocation problem. Intelligent Systems Engineering 1, 1, 76–83.Google Scholar
Ralphs, T., Shinano, Y., Berthold, T. and Koch, T. 2017. Parallel solvers for mixed integer linear optimization. Tech. Rep. COR@L Technical Report 16T-014-R3, Lehigh University.Google Scholar
Rao, V. and Kumar, V. 1988. Superlinear speedup in parallel state-space search. In Proc. of Foundations of Software Technology and Theoretical Computer Science. 161–174.Google Scholar
Reynolds, J. C. 1993. The discoveries of continuations. LISP and Symbolic Computation 6, 3/4, 233–247.Google Scholar
Rice, J. R. 1976. The algorithm selection problem. Advances in Computers 15, 65–118.Google Scholar
Rolf, C. and Kuchcinski, K. 2010. Combining parallel search and parallel consistency in constraint programming. In Proc. of 3rd Workshop on Techniques for Implementing Constraint Programming Systems. 38–52.Google Scholar
Rossi, F., vanBeek, P. Beek, P. and Walsh, T., Eds. 2006. Handbook of Constraint Programming. Elsevier Science.Google Scholar
Roussel, O. 2011. Description of ppfolio. Tech. rep.Centre de Recherche en Informatique de Lens. URL: http://www.cril.univ-artois.fr/~roussel/ppfolio/solver1.pdfGoogle Scholar
Ruiz-Andino, A., Araujo, L., Sáenz, F. and Ruz, J. J. 1998. Parallel arc-consistency for functional constraints. In Proc. of Workshop on Implementation Technology for Programming Languages based on Logic, ICLP. 86–100.Google Scholar
Salido, M. A. and Barber, F. 2006. Distributed CSPs by graph partitioning. Applied Mathematics and Computation 183, 1, 491–498.Google Scholar
Saraswat, V. A. and Rinard, M. 1990. Concurrent constraint programming. In Proc. of the 17th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York, NY, USA, 232–245.Google Scholar
Sassi, N., Salah, K. B. and Ghédira, K. 2017. DOC-BRelax: A new multi-agent system to solve distributed constraint optimization problems. Future Generation Computer Systems 73, 44–51.Google Scholar
Schubert, T., Lewis, M. and Becker, B. 2009. PaMiraXT: Parallel sat solving with threads and message passing. Journal on Satisfiability, Boolean Modeling and Computation 6, 203–222.Google Scholar
Schulte, C. 2000. Parallel search made simple. In Proc. of the 1st Workshop on Techniques for Implementing Constraint Programming Systems. 41–57.Google Scholar
Singer, D. 2006. Parallel resolution of the satisfiability problem: A survey. In Parallel Combinatorial Optimization, E.-G. Talbi, Ed. Wiley, 123–147.Google Scholar
Smith-Miles, K. A. 2009. Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Computing Surveys (CSUR) 41, 1, 6:1–6:25.Google Scholar
Sun, X.-H. and Chen, Y. 2010. Reevaluating Amdahl's law in the multicore era. Journal of Parallel and Distributed Computing 70, 2, 183–188.Google Scholar
VanHentenryck, P. Hentenryck, P. and Michel, L. 2009. Constraint-Based Local Search. The MIT Press.Google Scholar
VanRoy, P. Roy, P. and Haridi, S. 1999. Mozart: A programming system for agent applications. AgentLink News 4, 3–8.Google Scholar
Verhoeven, M. G. A. and Aarts, E. H. L. 1995. Parallel local search. Journal of Heuristics 1, 43–65.Google Scholar
Wahbi, M. and Brown, K. N. 2014. Global constraints in distributed CSP: Concurrent GAC and explanations in ABT. In Proc. of Principles and Practice of Constraint Programming: 20th International Conference, Lyon, France, September 8–12, 2014. 721–737.Google Scholar
Wang, C. J. and Tsang, E. P. K. 1991. Solving constraint satisfaction problems using neural networks. In Proc. of the 2nd International Conference on Artificial Neural Networks. IET, 295–299.Google Scholar
Wang, C. J. and Tsang, E. P. K. 1992. A cascadable VLSI design for GENET. In Proc. of International Workshop on VLSI for Neural Networks and Artificial Intelligence, Oxford.Google Scholar
Wetter, J., Akgün, Ö. and Miguel, I. 2015. Automatically generating streamlined constraint models with ESSENCE and CONJURE. In Proc. of International Conference on Principles and Practice of Constraint Programming. Springer, 480–496.Google Scholar
Wotzlaw, A., vander Grinten, A. der Grinten, A., Speckenmeyer, E. and Porschen, S. 2012. pfolioUZK: Solver description. Proc. of SAT Challenge 2012: Solver and Benchmark Descriptions, 45.Google Scholar
Xie, F. and Davenport, A. J. 2010. Massively parallel constraint programming for supercomputers: Challenges and initial results. In Proc. of 7th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Bologna, Italy, June 14–18, 2010, Lodi, A., Milano, M. and Toth, P., Eds. Lecture Notes in Computer Science, vol. 6140. Springer, 334–338.Google Scholar
Xu, L., Hutter, F., Hoos, H. H. and Leyton-Brown, K. 2008. SATzilla: Portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research 32, 565–606.Google Scholar
Yokoo, M. and Hirayama, K. 2000. Algorithms for distributed constraint satisfaction: A review. Autonomous Agents and Multi-Agent Systems 3, 2, 185–207.Google Scholar
Yokoo, M., Ishida, T., Durfee, E. H. and Kuwabara, K. 1992. Distributed constraint satisfaction for formalizing distributed problem solving. In Proc. of the 12th International Conference on Distributed Computing Systems. IEEE, 614–621.Google Scholar
Yun, X. and Epstein, S. L. 2012. Learning algorithm portfolios for parallel execution. In Learning and Intelligent Optimization. Springer, Berlin, Heidelberg, 323–338.Google Scholar
Zhang, W., Wang, G., Xing, Z. and Wittenburg, L. 2005. Distributed stochastic search and distributed breakout: Properties, comparison and applications to constraint optimization problems in sensor networks. Artificial Intelligence 161, 1, 55–87.Google Scholar
Zhang, Y. and Mackworth, A. K. 1991. Parallel and distributed algorithms for finite constraint satisfaction problems. In Proc. of the 3rd IEEE Symposium on Parallel and Distributed Processing. 394–397.Google Scholar
Zivan, R., Yedidsion, H., Okamoto, S., Glinton, R. and Sycara, K. 2015. Distributed constraint optimization for teams of mobile sensing agents. Autonomous Agents and Multi-Agent Systems 29, 3, 495–536.Google Scholar
Zoeteweij, P. and Arbab, F. 2004. A component-based parallel constraint solver. In Proc. of the 6th International Conference on Coordination Models and Languages. 307–322.Google Scholar