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Watched Literals for Constraint Propagation in Minion [chapter]

Ian P. Gent, Chris Jefferson, Ian Miguel
2006 Lecture Notes in Computer Science  
We describe three important aspects of watched literals as we apply them to constraints, and how they are implemented in the Minion constraint solver.  ...  We show that watched literals, already a great success in the satisfiability community, can be used to provide highly efficient implementations of constraint propagators.  ...  Implementing Watched Literals in Minion We report briefly on our infrastructure for watched literals in Minion.  ... 
doi:10.1007/11889205_15 fatcat:wa5p54zhrfgczjy66za52rpgfy

Implementing logical connectives in constraint programming

Christopher Jefferson, Neil C.A. Moore, Peter Nightingale, Karen E. Petrie
2010 Artificial Intelligence  
By extending the OR propagator, we present a propagator for ATLEASTK, which expresses that at least k of its child constraints are satisfied in any solution.  ...  A key reason for the success of Boolean Satisfiability (SAT) solvers is their ability to propagate OR constraints efficiently, making use of movable triggers.  ...  Acknowledgements We would like to thank the anonymous reviewers for their helpful comments about an earlier version of this paper.  ... 
doi:10.1016/j.artint.2010.07.001 fatcat:5iyuikpmpfhanh4u77sddmhf3u

An empirical study of learning and forgetting constraints

Ian P. Gent, Ian Miguel, Neil C.A. Moore
2012 AI Communications  
Received wisdom states that a small number of learned constraints do the majority of propagation in learning solvers, yet we are aware of no published evidence substantiating this view.  ...  We conduct a major empirical investigation into the overheads introduced by unbounded constraint learning in CSP. To the best of our knowledge, this is the first published study in either CSP or SAT.  ...  The design of watched literal propagators make it possible that constraints that do not propagate will cost the solver very little in time.  ... 
doi:10.3233/aic-2012-0524 fatcat:pmnlmyuz7jesrml3cl2lpg7jgu

Generalised arc consistency for the AllDifferent constraint: An empirical survey

Ian P. Gent, Ian Miguel, Peter Nightingale
2008 Artificial Intelligence  
The AllDifferent constraint is a crucial component of any constraint toolkit, language or solver, since it is very widely used in a variety of constraint models.  ...  This work is an analytical survey of optimizations of the main algorithm for GAC for the AllDifferent constraint. We evaluate empirically a number of key techniques from the literature.  ...  We would like to thank Chris Jefferson for technical help with development in Minion [9] and helpful discussion, Andrea Rendl for use of Tailor [12] , and Max Neunhöffer for useful discussion of data  ... 
doi:10.1016/j.artint.2008.10.006 fatcat:23nirhwbqnfzlanlj6thzgsxci

Generating Special-Purpose Stateless Propagators for Arbitrary Constraints [chapter]

Ian P. Gent, Chris Jefferson, Ian Miguel, Peter Nightingale
2010 Lecture Notes in Computer Science  
Propagation is so fast that, for constraints available in our solver, the generated propagator compares well with a human-optimised propagator for the same constraint.  ...  The technique can also be many times faster than a decomposition into primitive constraints in the Minion solver.  ...  Therefore any literals in S which are removed by a GAC propagator for SD would also be removed by a GAC propagator for S. We now show no extra literals would be removed by a GAC propagator for S.  ... 
doi:10.1007/978-3-642-15396-9_19 fatcat:pzv6uhazsfb7vhh5eyk7xf5s4i

The Semigroups of Order 10 [chapter]

Andreas Distler, Chris Jefferson, Tom Kelsey, Lars Kotthoff
2012 Lecture Notes in Computer Science  
This solves a previously open problem in Mathematics, and has directly led to improvements in Constraint Satisfaction technology.  ...  We describe the use of mathematical results combined with distributed Constraint Satisfaction to show that the number of non-equivalent semigroups of order 10 is 12,418,001,077,381,302,684.  ...  Parts of the computational resources for this project were provided by an Amazon Web Services research grant.  ... 
doi:10.1007/978-3-642-33558-7_63 fatcat:gta7rsguaneldi2frsupkxpe4e

An automated approach to generating efficient constraint solvers

Dharini Balasubramaniam, Christopher Jefferson, Lars Kotthoff, Ian Miguel, Peter Nightingale
2012 2012 34th International Conference on Software Engineering (ICSE)  
Combinatorial problems appear in numerous settings, from timetabling to industrial design. Constraint solving aims to find solutions to such problems efficiently and automatically.  ...  Current constraint solvers are monolithic in design, accepting a broad range of problems. The cost of this convenience is a complex architecture, inhibiting efficiency, extensibility and scalability.  ...  ACKNOWLEDGMENT This work is supported by the EPSRC grant 'A Constraint Solver Synthesiser' (EP/H004092/1) and SICSA studentships.  ... 
doi:10.1109/icse.2012.6227151 dblp:conf/icse/BalasubramaniamJKMN12 fatcat:oo6uvb4xyff3lpdhodwc7gsiqy

Generalized Support and Formal Development of Constraint Propagators [article]

James Caldwell and Ian P. Gent and Peter Nightingale
2016 arXiv   pre-print
Specialised propagation algorithms (propagators) exist for many classes of constraints. The concept of support is pervasive in the design of propagators.  ...  Derived algorithms may make use of dynamic literal triggers or watched literals for efficiency. Finally, two case studies of deriving efficient algorithms are given.  ...  Acknowledgements The work of the authors has been partially supported by the following UK EPSRC grants: EP/E030394/1, EP/F031114/1, EP/H004092/1, and EP/M003728/1, support for which we are very grateful  ... 
arXiv:1504.05846v2 fatcat:hk6lnwqvinewnf3ny2mlgcda4u

Generalized support and formal development of constraint propagators

James Caldwell, Ian P. Gent, Peter Nightingale
2017 AI Communications  
Specialized propagation algorithms (propagators) exist for many classes of constraints. The concept of support is pervasive in the design of propagators.  ...  Derived algorithms may make use of dynamic literal triggers or watched literals [15] for efficiency. Finally, three case studies of deriving efficient algorithms are given.  ...  Acknowledgements The work of the authors has been partially supported by the following UK EPSRC grants: EP/E030394/1, EP/F031114/1, EP/H004092/1, and EP/M003728/1, support for which we are very grateful  ... 
doi:10.3233/aic-170740 fatcat:7wgvmjjmwjgm3j4dltuh3yo57m

Savile Row Manual [article]

Peter Nightingale
2021 arXiv   pre-print
Savile Row translates a solver-independent constraint modelling language to the input languages for various solvers including constraint, SAT, and SMT solvers.  ...  We describe the constraint modelling tool Savile Row, its input language and its main features.  ...  The model produced is not entirely flat, it makes use of nested watched-or and watched-and constraints. • Gecode -Output is produced for Gecode in the entirely flat, instance-level language FlatZinc for  ... 
arXiv:2201.03472v1 fatcat:lztbtkbiljfbdkssn34t565afi

Lazy Explanations for Constraint Propagators [chapter]

Ian P. Gent, Ian Miguel, Neil C. A. Moore
2010 Lecture Notes in Computer Science  
Explanations are a technique for reasoning about constraint propagation, which have been applied in many learning, backjumping and user-interaction algorithms for constraint programming.  ...  To date explanations for constraints have usually been recorded eagerly when constraint propagation happens, which leads to inecient use of time and space, because many will never be used.  ...  Learned clauses are propagated by the 2-watch literal scheme [21] .  ... 
doi:10.1007/978-3-642-11503-5_19 fatcat:h32w7yc33nhlxheq3ssvncqaze

Constraint solvers: An empirical evaluation of design decisions [article]

Lars Kotthoff
2010 arXiv   pre-print
This paper presents an evaluation of the design decisions made in four state-of-the-art constraint solvers; Choco, ECLiPSe, Gecode, and Minion.  ...  The analysis of the impact of the design decisions focuses on the different ways of memory management, behaviour with increasing problem size, and specialised algorithms for specific types of variables  ...  Thanks also go to Warwick Harvey for modelling the Social Golfers problem in ECLiPSe and Mikael Lagerkvist for pointing out a mistake in an earlier version of this paper.  ... 
arXiv:1002.0134v1 fatcat:i5b7kby5jfagvnvhpg3noylfoe

Optimal Implementation of Watched Literals and More General Techniques

I. P. Gent
2013 The Journal of Artificial Intelligence Research  
The result applies to a simple general framework, which I present: applications include watched literal unit propagation in SAT and a number of examples in constraint satisfaction.  ...  Techniques like watched literals are known to be highly space efficient and effective in practice.  ...  Acknowledgments I thank Chris Jefferson and Peter Nightingale for help with this paper in many ways, for example C++ coding advice and suggestions on how to implement variants of watched literals in MiniSat  ... 
doi:10.1613/jair.4016 fatcat:wnq2vlr3vne6bby4iycvflafmq

Maintaining State in Propagation Solvers [chapter]

Raphael M. Reischuk, Christian Schulte, Peter J. Stuckey, Guido Tack
2009 Lecture Notes in Computer Science  
Constraint propagation solvers interleave propagation, removing impossible values from variable domains, with search. The solver state is modified during propagation.  ...  This paper sets out the possible ways in which a propagation solver can choose to maintain state, and the restrictions that such choices place on the resulting system.  ...  We thank Thibaut Feydy and Sebastian Brand for many interesting discussions related to this work.  ... 
doi:10.1007/978-3-642-04244-7_54 fatcat:3t72mnyzafhefikijtlma56boe

Short and Long Supports for Constraint Propagation

P. Nightingale, I. P. Gent, C. Jefferson, I. Miguel
2013 The Journal of Artificial Intelligence Research  
All the proposed algorithms are excellent for propagating disjunctions of constraints.  ...  propagation algorithm for exploiting short supports.  ...  Acknowledgements We would like to thank anonymous reviewers of our previous papers on this topic for their comments, and EPSRC for funding this work through grants EP/H004092/1 and EP/E030394/1.  ... 
doi:10.1613/jair.3749 fatcat:oxsogjufofcf5a7o2jawndvmji
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