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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  
Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses.  ...  We show that this framework generalises certain known hybrid tractable classes.  ...  In general, we are not yet able to make any conjecture concerning a dichotomy for hybrid tractability defined by general forbidden patterns.  ... 
doi:10.1613/jair.3651 fatcat:6tfaqcsoeffu7oxfwrkj426wz4

Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination

Martin C. Cooper, Peter G. Jeavons, András Z. Salamon
2010 Artificial Intelligence  
In this paper we introduce the broken-triangle property, which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure.  ...  Considerable progress has been made in identifying properties which ensure tractability in such problems, such as the property of being tree-structured.  ...  tractable classes of binary CSP instances which significantly generalize tree-structured problems as well as previously-identified language-based classes.  ... 
doi:10.1016/j.artint.2010.03.002 fatcat:emwukrqjlfdphcydgqzrdcecsq

NeurASP: Embracing Neural Networks into Answer Set Programming

Zhun Yang, Adam Ishay, Joohyung Lee
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Such hybrid width parameters, which consider both the query structure and database content, are a natural avenue for further research.  ...  To tackle the problem beyond bounded arity, a number of generalizations of treewidth have been developed that provide sufficient conditions for tractably solving CSPs, the most important of which are hypertree  ... 
doi:10.24963/ijcai.2020/239 dblp:conf/ijcai/ChenGLP20 fatcat:m3inpryda5bphltwzyxclbvj3m

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.  ...  An important challenge is to identify tractable CSPs which can be solved efficiently.  ...  Broken-triangle new hybrid class With collaborators Martin Cooper and Peter Jeavons, I introduced a new tractable hybrid class that generalizes tree-structured CSPs.  ... 
doi:10.1007/s10601-015-9224-8 fatcat:lollakqzx5h7xeajtfrmaz6u4q

Some New Tractable Classes of CSPs and Their Relations with Backtracking Algorithms [chapter]

Achref El Mouelhi, Philippe Jégou, Cyril Terrioux, Bruno Zanuttini
2013 Lecture Notes in Computer Science  
By relating the complexity of CSP algorithms to graph-theoretical parameters, our analysis allows us to define new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial  ...  So, our approach allows us to propose new tractable classes of CSPs that are naturally exploited by solvers, which indicates new ways to explain in some cases the practical efficiency of classical search  ...  like to thank Maria Chudnovsky for their fruitful discussion, about graph theory, perfect graphs and links with classes of graphs related to the clique problem, and the links with the microstructure of CSPs  ... 
doi:10.1007/978-3-642-38171-3_5 fatcat:nnkgshgetzhophuqvxhwv4njhy

A New Hybrid Tractable Class of Soft Constraint Problems [chapter]

Martin C. Cooper, Stanislav Živný
2010 Lecture Notes in Computer Science  
The constraint satisfaction problem (CSP) is a central generic problem in artificial intelligence.  ...  In this paper we study hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but properties which do not depend only on  ...  theory assumptions) are structures of bounded tree-width [17] .  ... 
doi:10.1007/978-3-642-15396-9_15 fatcat:uz2h3ndrw5dcra2phvo5xzfqna

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
Forbidding a finite set of patterns as topological minors also captures all other tractable structural restrictions of the binary CSP.  ...  This captures some tractable classes of the CSP, but does not capture classes defined by language restrictions, or the well-known structural property of acyclicity.  ...  new hybrid tractable classes that cannot be captured as either structural classes or language classes.  ... 
arXiv:1608.05358v2 fatcat:sgaphwoh6rh4xle6xvvmjcclua

A Microstructure-Based Family of Tractable Classes for CSPs [chapter]

Martin C. Cooper, Philippe Jégou, Cyril Terrioux
2015 Lecture Notes in Computer Science  
In this context, the Broken Triangle Property (BTP) is a state-of-the-art microstructure-based tractable class which generalizes well-known and previously-defined tractable classes, notably the set of  ...  In this paper, we propose to extend and to generalize this class using a more general approach based on a parameter k which is a given constant.  ...  This class strictly contains both structural tractable classes (such as tree-structured CSPs) and tractable classes defined by language restrictions.  ... 
doi:10.1007/978-3-319-23219-5_6 fatcat:uris5oeuiffr7afzrz4evmk3ka

A Join-Based Hybrid Parameter for Constraint Satisfaction [article]

Robert Ganian, Sebastian Ordyniak, Stefan Szeider
2019 arXiv   pre-print
It has, therefore, the potential to capture larger classes of tractable instances than purely structural parameters like hypertree width and the more general fractional hypertree width (fhtw).  ...  Joinwidth is a hybrid parameter, as it takes both the graphical structure as well as the constraint relations that appear in the instance into account.  ...  Bounded fractional hypertree width is the most general known structural restriction that gives rise to polynomial-time tractability of CSP.  ... 
arXiv:1907.12335v1 fatcat:q34osf6hvzes7hvwfurhqcmvhq

A Join-Based Hybrid Parameter for Constraint Satisfaction [chapter]

Robert Ganian, Sebastian Ordyniak, Stefan Szeider
2019 Lecture Notes in Computer Science  
It has, therefore, the potential to capture larger classes of tractable instances than purely structural parameters like hypertree width and the more general fractional hypertree width (fhtw).  ...  Joinwidth is a hybrid parameter, as it takes both the graphical structure as well as the constraint relations that appear in the instance into account.  ...  Bounded fractional hypertree width is the most general known structural restriction that gives rise to polynomial-time tractability of CSP.  ... 
doi:10.1007/978-3-030-30048-7_12 fatcat:dydl7jwmxfcjvn5mp5wrsbyi3a

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
This research direction develops at an impressive speed, regularly producing very strong and general results.  ...  probability theory, graph theory, and combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP  ...  The so-called "hybrid" tractability in CSP, which is tractability that cannot be attributed to a constraint language restriction or to a structural restriction alone, has not received a great deal of attention  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

A Hybrid Tractable Class for Non-binary CSPs

Achref El Mouelhi, Philippe Jegou, Cyril Terrioux
2013 2013 IEEE 25th International Conference on Tools with Artificial Intelligence  
The concept of hybrid tractable class, which allows to deal simultaneously with the restrictions of languages and, for example, the satisfaction of structural properties, is an approach which has already  ...  Here we study a hybrid class for non-binary CSPs. With this aim in view, we consider the tractable class BTP introduced in [1].  ...  In this paper, we study a hybrid tractable class called DBTP for Dual Broken Triangle Property. So, this class is based on the concept of "Broken Triangle" which is the basis of BTP.  ... 
doi:10.1109/ictai.2013.144 dblp:conf/ictai/MouelhiJT13 fatcat:spli7k3dczeydozgrncmumq5qq

Constraint Satisfaction Problems and Finite Algebras [chapter]

Andrei A. Bulatov, Andrei A. Krokhin, Peter Jeavons
2000 Lecture Notes in Computer Science  
For example, it is known that for any finite constraint language Γ, and any k, if one restricts instances of CSP(Γ) to those of tree-width k then the problem class is tractable.  ...  Indeed, several of the most general tractability results to date can be expressed in this manner.  ... 
doi:10.1007/3-540-45022-x_24 fatcat:egghegcdyrfofnzw7dgd67cqdy

A hybrid tractable class for non-binary CSPs

Achref El Mouelhi, Philippe Jégou, Cyril Terrioux
2015 Constraints  
The concept of hybrid tractable class, which allows to deal simultaneously with the restrictions of languages and, for example, the satisfaction of structural properties, is an approach which has already  ...  Find new islands of tractability, that is classes of CSP instances for which polytime algorithms exist, is a fundamental task in the study of constraint satisfaction problems.  ...  Links with the solving Generally, the instances of a given tractable class are solved thanks to a specific algorithm which is dedicated to this particular tractable class.  ... 
doi:10.1007/s10601-015-9185-y fatcat:k2th3wp67zf5dhd7zkhugmuhdy

Hybrid tractability of valued constraint problems

Martin C. Cooper, Stanislav Živný
2011 Artificial Intelligence  
In this work, we initiate the study of hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but which do not depend only  ...  on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity).  ...  which will eventually cover structural, language and hybrid reasons for tractability.  ... 
doi:10.1016/j.artint.2011.02.003 fatcat:otqplqno5fah3if7z2f4gc2zaq
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