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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.  ...  Lazy explanations for constraint propagators In this section we describe how specic constraint propagators can be made to produce lazy explanations, specically, what they need to store at propagationtime  ... 
doi:10.1007/978-3-642-11503-5_19 fatcat:h32w7yc33nhlxheq3ssvncqaze

Lazy Clause Generation: Combining the Power of SAT and CP (and MIP?) Solving [chapter]

Peter J. Stuckey
2010 Lecture Notes in Computer Science  
constraints, as well as programming the search for solutions to take into account problem structure.  ...  Finite domain propagation solving, the basis of constraint programming (CP) solvers, allows building very high-level models of problems, and using highly specific inference encapsulated in complex global  ...  For each propagator we have to determine how to efficiently determine explanations of each propagation, and which form the explanation should take.  ... 
doi:10.1007/978-3-642-13520-0_3 fatcat:bwlxjkj54vfwxhoqmtnd4i3hmy

Lazy Clause Generation Reengineered [chapter]

Thibaut Feydy, Peter J. Stuckey
2009 Lecture Notes in Computer Science  
In lazy clause generation finite domain propagators are considered as clause generators that create a SAT description of their behaviour for a SAT solver.  ...  The original implementation of lazy clause generation was constructed as a cut down finite domain propagation engine inside a SAT solver.  ...  Global propagators Rather than create complex explanations for global constraints it is usually easier to build decompositions.  ... 
doi:10.1007/978-3-642-04244-7_29 fatcat:epaszfug5vdhnfhw4h6lgp7sv4

Conflict Directed Lazy Decomposition [chapter]

Ignasi Abío, Peter J. Stuckey
2012 Lecture Notes in Computer Science  
literals for explanation.  ...  ) propagate the complex constraint using a standalone algorithm and explain the propagation.  ...  Lazy Decomposition Propagator for Cardinality Constraints In this section we describe the LD propagator for a cardinality constraint of the form x 1 + x 2 + . . . + x n K.  ... 
doi:10.1007/978-3-642-33558-7_8 fatcat:otqdiowp5bgy5bvu7k44bgu4ce

Explaining the cumulative propagator

Andreas Schutt, Thibaut Feydy, Peter J. Stuckey, Mark G. Wallace
2010 Constraints  
The global cumulative constraint was proposed for modelling cumulative resources in scheduling problems for finite domain (FD) propagation.  ...  In this article we show how, once we use lazy clause generation, modelling the cumulative constraint by decomposition creates a highly competitive version of cumulative.  ...  Acknowledgements We would like to thank Phillipe Baptiste for suggesting this line of enquiry.  ... 
doi:10.1007/s10601-010-9103-2 fatcat:lf3cfhovbzfurjbyw6plutwbxi

Explaining circuit propagation

Kathryn Glenn Francis, Peter J. Stuckey
2013 Constraints  
Even though the most powerful propagator considered for circuit and variants creates huge explanations, we find that explanation is highly advantageous for solving problems involving this kind of constraint  ...  In this paper we examine how to integrate the circuit constraint, and its variants, into a lazy clause generation solver. To do so we must extend the constraint to explain its propagation.  ...  Acknowledgments We are thankful to the reviewers for their helpful comments and suggestions.  ... 
doi:10.1007/s10601-013-9148-0 fatcat:yqphqyc2ybh53g7sq6mgjegif4

Two Clause Learning Approaches for Disjunctive Scheduling [chapter]

Mohamed Siala, Christian Artigues, Emmanuel Hebrard
2015 Lecture Notes in Computer Science  
In particular this approach is very efficient for proving unfeasibility.  ...  We first describe an alternative method for handling lazily generated atoms without computational overhead. Next, we propose a novel conflict analysis scheme tailored for disjunctive scheduling.  ...  The authors would like to thank the Insight Centre for Data Analytics for kindly granting us access to its computational resources.  ... 
doi:10.1007/978-3-319-23219-5_28 fatcat:dvs2jfgqzzdxfiafdggxcsmgzy

Explaining Propagators for String Edit Distance Constraints

Felix Winter, Nysret Musliu, Peter Stuckey
Furthermore, we describe a propagation algorithm and investigate an explanation strategy for an edit distance constraint propagator that can be incorporated into state of the art lazy clause generation  ...  In this work, we propose a novel global constraint to formulate restrictions on the minimum edit distance for such problems.  ...  Acknowledgments The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged.  ... 
doi:10.1609/aaai.v34i02.5530 fatcat:7m2mko4hcfexnemhwxagwyfs2y

Explaining Flow-Based Propagation [chapter]

Nicholas Downing, Thibaut Feydy, Peter J. Stuckey
2012 Lecture Notes in Computer Science  
Lazy clause generation is a powerful approach to reducing search in constraint programming. For use in a lazy clause generation solver, global constraints must be extended to explain themselves.  ...  In this paper we present two new generic flow-based propagators (for hard and soft flow-based constraints) with several novel features, and most importantly, the addition of explanation capability.  ...  This research aimed at drawing together the previous work on flow-based alldifferent and gcc constraints [18] , generic flow networks [2, 22] and explanations for flows [12, 20] and general LPs [  ... 
doi:10.1007/978-3-642-29828-8_10 fatcat:vecpscf3xbe2jpkgjqnonfdiru

Inter-instance Nogood Learning in Constraint Programming [chapter]

Geoffrey Chu, Peter J. Stuckey
2012 Lecture Notes in Computer Science  
Lazy Clause Generation is a powerful approach to reducing search in Constraint Programming.  ...  This is achieved by recording sets of domain restrictions that previously led to failure as new clausal propagators called nogoods.  ...  Finite domain propagation is instrumented to record an explanation for each inference.  ... 
doi:10.1007/978-3-642-33558-7_19 fatcat:mnrgml33unelfj2yqn5doh6xjq

Why Cumulative Decomposition Is Not as Bad as It Sounds [chapter]

Andreas Schutt, Thibaut Feydy, Peter J. Stuckey, Mark G. Wallace
2009 Lecture Notes in Computer Science  
The global cumulative constraint was proposed for modelling cumulative resources in scheduling problems for finite domain (FD) propagation.  ...  In this paper we show that using lazy clause generation where we model cumulative constraint by decomposition gives a very competitive implementation of cumulative resource problems.  ...  We would like to thank Phillipe Baptiste for suggesting this line of enquiry.  ... 
doi:10.1007/978-3-642-04244-7_58 fatcat:aaxuxjb5wffbda5dytrcpif24e

To Encode or to Propagate? The Best Choice for Each Constraint in SAT [chapter]

Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, Peter J. Stuckey
2013 Lecture Notes in Computer Science  
For example, given a cardinality constraint x1 + . . . + xn ≤ k, as soon as k variables become true, such a propagator can set the remaining variables to false, generating a so-called explanation clause  ...  Alternatively, for instances with many (or large) constraints, the SAT solver can also be extended with built-in propagators (the SAT Modulo Theories approach, SMT).  ...  Another possibility for future work concerns the version of SMT in which explanation clauses are generated and learned immediately when a constraint propagates, as in the initial version of Lazy Clause  ... 
doi:10.1007/978-3-642-40627-0_10 fatcat:oafazwrkpjdthego53vqdf7j44

An Experimental Evaluation of Ground Decision Procedures [chapter]

Leonardo de Moura, Harald Rueß
2004 Lecture Notes in Computer Science  
There is a large variety of algorithms for ground decision procedures, but their differences, in particular in terms of experimental performance, are not well studied.  ...  Insufficient constraint propagation in lazy integrations.  ...  propagation (transitivity), but none of the existing lazy provers propagates this inference.  ... 
doi:10.1007/978-3-540-27813-9_13 fatcat:vtodfjv6mrcknhl4vghsmdxvti

Explaining Propagators for Edge-Valued Decision Diagrams [chapter]

Graeme Gange, Peter J. Stuckey, Pascal Van Hentenryck
2013 Lecture Notes in Computer Science  
In this paper we show how to add explanation to the cost-mdd propagator.  ...  The cost-mdd constraint is a generic propagator for reasoning about reachability in a multi-decision diagram with costs attached to edges (a generalization of cost-regular).  ...  In this paper we investigate how to incorporate cost-mdd global propagators into a lazy clause generation [8] based constraint solver.  ... 
doi:10.1007/978-3-642-40627-0_28 fatcat:mft7lvo6sfakxhnhaduscz4e5a

Predicate learning and selective theory deduction for a difference logic solver

Chao Wang, A. Gupta, M. Ganai
2006 Proceedings - Design Automation Conference  
Our new optimization techniques include flexible theory constraint propagation, selective theory deduction, and dynamic predicate learning. We have implemented these techniques in our lazy solver.  ...  We use the lazy approach by combining a DPLL Boolean SAT procedure with a dedicated graph-based theory solver, which adds transitivity constraints among difference predicates on a "need-to" basis.  ...  Efficient Theory Constraint Propagation First, we give experimental results on the different settings for invoking theory constraint propagation.  ... 
doi:10.1109/dac.2006.229207 fatcat:pp3kmlfj7zbijlxkkpb4kzajvm
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