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On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

Clément Carbonnel, David A. Cohen, Martin C. Cooper, Stanislav Živný
2018 Algorithmica  
We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints.  ...  We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT.  ...  An interesting research direction is to study those monotone classes defined by a forbidden pattern which are solved by singleton arc consistency, both in order to uncover new tractable classes and to  ... 
doi:10.1007/s00453-018-0498-2 pmid:31007327 pmcid:PMC6449328 fatcat:hexfkxyuh5awngv76xkzamhqze

On Singleton Arc Consistency for CSPs Defined by Monotone Patterns [article]

Clement Carbonnel and David A. Cohen and Martin C. Cooper and Stanislav Zivny
2018 arXiv   pre-print
We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints.  ...  We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT.  ...  An interesting research direction is to study those monotone classes defined by a forbidden pattern which are solved by singleton arc consistency, both in order to uncover new tractable classes and to  ... 
arXiv:1704.06215v4 fatcat:q4bwigjw5jashh3beedms63lwa

Characterising the complexity of constraint satisfaction problems defined by 2-constraint forbidden patterns

Martin C. Cooper, Guillaume Escamocher
2015 Discrete Applied Mathematics  
For example, Y consists of 4 points a . Y also occurs in X by a merging followed by an extension. Notation. Let P be a CSP pattern.  ...  We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints.  ...  Another interesting avenue for research is to enrich the language of forbidden patterns, as we have done for existential patterns.  ... 
doi:10.1016/j.dam.2014.10.035 fatcat:vbursdr47ngepatajiudv5ggcy

Binary Constraint Satisfaction Problems Defined by Excluded Topological Minors [article]

David A. Cohen, Martin C. Cooper, Peter G. Jeavons, Stanislav Zivny
2018 arXiv   pre-print
We consider subproblems defined by restricting the allowed form of this graph. One type of restriction that has previously been considered is to forbid certain specified substructures (patterns).  ...  By forbidding a finite set of patterns from occurring as topological minors we obtain a compact mechanism for expressing novel tractable subproblems of the binary CSP, including new generalisations of  ...  Since I is singleton arc-consistent, I[N ] is arc-consistent. Let J ′ = be the augmented pattern shown in Figure 14. Note that J ′ = SP → Patt(C 3 ) = .  ... 
arXiv:1608.05358v2 fatcat:sgaphwoh6rh4xle6xvvmjcclua

The Tractability of CSP Classes Defined by Forbidden Patterns

D. A. Cohen, M. C. Cooper, P. Creed, D. Marx, A. Z. Salamon
2012 The Journal of Artificial Intelligence Research  
Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic sub-problems).  ...  We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns.  ...  By defining a natural notion of containment of patterns in a CSP, we are able to describe problems defined by forbidden patterns: a class of CSP instances defined by forbidding a particular pattern χ are  ... 
doi:10.1613/jair.3651 fatcat:6tfaqcsoeffu7oxfwrkj426wz4

A Dichotomy for 2-Constraint Forbidden CSP Patterns [article]

Martin C. Cooper, Guillaume Escamocher
2012 arXiv   pre-print
We demonstrate a dichotomy in the case of forbidden patterns consisting of either one or two constraints.  ...  The complete characterisation of all tractable classes defined by forbidding patterns (where a pattern is simply a compact representation of a set of subproblems) is a challenging problem.  ...  By arc consistency, we have a ′ 0 then a point in A v can be compatible with only one point in A v ′ .  ... 
arXiv:1201.3868v1 fatcat:3itmaekgw5e4zfu4j2txpintp4

Colouring, constraint satisfaction, and complexity

Pavol Hell, Jaroslav Nešetřil
2008 Computer Science Review  
However, for general constraint satisfaction problems, dichotomy has only been conjectured.  ...  Similar dichotomy has been proved for the class of graph homomorphism problems, which are intermediate problems between graph colouring and constraint satisfaction.  ...  Indeed, much of the current research on the Dichotomy Conjecture amounts to a hunt for new polynomial algorithms. We are grateful to G. Kun and M. Szegedy, as well as to M.  ... 
doi:10.1016/j.cosrev.2008.10.003 fatcat:ttj3i4ajvnauhe4iyuqy2qpfni

Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems

Martin C. Cooper, Aymeric Duchein, Achref El Mouelhi, Guillaume Escamocher, Cyril Terrioux, Bruno Zanuttini
2016 Artificial Intelligence  
A directional version of general-arity BTP-merging then allows us to extend the BTP tractable class previously defined only for binary CSP.  ...  Extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems.  ...  Acknowledgments This research was supported by ANR Project ANR-10-BLAN-0210. Martin Cooper was also supported by EPSRC grant EP/L021226/1.  ... 
doi:10.1016/j.artint.2016.02.001 fatcat:4tjdrvoym5d7np3uf6katcik5u

Galois Connections for Patterns: An Algebra of Labelled Graphs [chapter]

David A. Cohen, Martin C. Cooper, Peter G. Jeavons, Stanislav Živný
2021 Lecture Notes in Computer Science  
The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP.  ...  Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be  ...  The European Union is not liable for any use that may be made of the information contained therein.  ... 
doi:10.1007/978-3-030-72308-8_9 fatcat:oz44glrizjgoza2jvvwmohti7e

Basic Techniques for Creating an Efficient CSP Solver

C. Frăsinaru
2007 Scientific Annals of Computer Science  
This paper presents from both theoretical and practical points of view the design of a general purpose CSP solver.  ...  Many computationally difficult problems from areas like planning and scheduling are easily modelled as constraint satisfaction problems (CSP).  ...  We conceived our solver based on the MVC (Model-View-Controller) design pattern [10] , [26] : • Model layer -offers the instruments for modelling a problem as a CSP instance; • Control layer -contains  ... 
doaj:cc6558048fb848dba6c1c02071553a61 fatcat:jo74wsucmnfd7bky7vchpz6lze

Transformations of representation in constraint satisfaction

András Z. Salamon
2015 Constraints  
My main contribution is an investigation of such hybrid CSPs which cannot be defined with either one of these kinds of restrictions.  ...  For the common case where all constraints involve only two variables, I show how the microstructure can be used to define CSPs that are tractable because their clause structures fall within classes of  ...  These CSPs correspond naturally to the partial progress of a constraint solver during search. Moreover, hereditary CSPs can be defined by a set of forbidden substructures in the microstructure.  ... 
doi:10.1007/s10601-015-9224-8 fatcat:lollakqzx5h7xeajtfrmaz6u4q

Tractability in constraint satisfaction problems: a survey

Clément Carbonnel, Martin C. Cooper
2015 Constraints  
Acknowledgments We are grateful to Peter Jeavons and StanislavŽivný for their detailed comments on a first draft of this paper, and to the reviewers for their constructive comments.  ...  Any class of instances defined by a forbidden pattern is necessarily recognisable in polynomial time by a simple exhaustive search for the pattern.  ...  It has been recently shown that singleton arc-consistency solves CSP(Γ ) when Γ admits a majority polymorphism [40] .  ... 
doi:10.1007/s10601-015-9198-6 fatcat:fl7kxmceh5bqzpyd2c37rtohii

New schemes for simplifying binary constraint satisfaction problems

Wady Naanaa
2018 Discrete Mathematics & Theoretical Computer Science  
for simplifying binary CSPs that allow the narrowing of valuedomains, either via value merging or via value suppression.  ...  This work contributes also to the theory of tractable CSPs byidentifying a new tractable class of binary CSP.  ...  And since we started from an arc consistent instance, that is P (0) , we deduce that all the instances defined by (5) are arc consistent.  ... 
doi:10.23638/dmtcs-22-1-10 fatcat:7jutpgd55zfrjgsi5g7xukwfmu

Variable elimination in binary CSPs [article]

Martin C. Cooper, Achref El Mouelhi, Cyril Terrioux
2019 arXiv   pre-print
We study variable-elimination rules based on the language of forbidden patterns enriched with counting and quantification over variables and values.  ...  We give optimised algorithms to apply these rules and show that each define a novel tractable class.  ...  Note that, in an arc-consistent instance, singleton-domain variables would be eliminated by all four of the rules we are comparing.  ... 
arXiv:1905.04209v1 fatcat:kjowvepsnngh5gn2xiax4x2a4q

Constraint Programming viewed as Rule-based Programming [article]

Krzysztof R. Apt, Eric Monfroy
2001 arXiv   pre-print
hyper-arc consistency in MS98b).  ...  The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called  ...  Acknowledgements We would like to thank Thom Frühwirth, Andrea Schaerf and all three referees for several useful suggestions. Victor Marek provided material for Section 3 and suggested Section 4.  ... 
arXiv:cs/0003076v2 fatcat:mi3xlavnwjbzlgmzw7fn3n53py
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