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Point-width and Max-CSPs [article]

Clement Carbonnel, Miguel Romero, Stanislav Zivny
2020 arXiv   pre-print
The complexity of (unbounded-arity) Max-CSPs under structural restrictions is poorly understood. The two most general hypergraph properties known to ensure tractability of Max-CSPs, β-acyclicity and bounded (incidence) MIM-width, are incomparable and lead to very different algorithms. We introduce the framework of point decompositions for hypergraphs and use it to derive a new sufficient condition for the tractability of (structurally restricted) Max-CSPs, which generalises both bounded
more » ... h and e̱ṯa̱-acyclicity. On the way, we give a new characterisation of bounded MIM-width and discuss other hypergraph properties which are relevant to the complexity of Max-CSPs, such as β-hypertreewidth.
arXiv:1904.07388v2 fatcat:efn7yqggmzd5tlx26u35xhrkjm

Tractability in constraint satisfaction problems: a survey

Clément Carbonnel, Martin C. Cooper
2015 Constraints  
doi:10.1007/s10601-015-9198-6 fatcat:fl7kxmceh5bqzpyd2c37rtohii

On Backdoors To Tractable Constraint Languages [article]

Clement Carbonnel, Martin C. Cooper, Emmanuel Hebrard
2014 arXiv   pre-print
In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong backdoor provides a reasonable decomposition of the original instance into easy instances. An important challenge is the design of algorithms that can find quickly a small strong backdoor if one exists. We present a systematic study of the parameterized complexity
more » ... backdoor detection when the target property is a restricted type of constraint language defined by means of a family of polymorphisms. In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the backdoor) unless P = NP or FPT = W[2]. When the parameter is k+r, however, we are able to identify large classes of languages for which the problem of finding a small backdoor is FPT.
arXiv:1404.3675v2 fatcat:tf2if2z3wjaprcezz247f7srn4

On Backdoors to Tractable Constraint Languages [chapter]

Clément Carbonnel, Martin C. Cooper, Emmanuel Hebrard
2014 Lecture Notes in Computer Science  
In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong backdoor provides a reasonable decomposition of the original instance into easy instances. An important challenge is the design of algorithms that can find quickly a small strong backdoor if one exists. We present a systematic study of the parameterized complexity
more » ... backdoor detection when the target property is a restricted type of constraint language defined by means of a family of polymorphisms. In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the backdoor) unless P = NP or FPT = W[2]. When the parameter is k + r, however, we are able to identify large classes of languages for which the problem of finding a small backdoor is FPT.
doi:10.1007/978-3-319-10428-7_18 fatcat:nvc6gx5oi5ew7gbsg2bj6ldx3i

The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable [article]

Clément Carbonnel
2016 arXiv   pre-print
Given a fixed constraint language Γ, the conservative CSP over Γ (denoted by c-CSP(Γ)) is a variant of CSP(Γ) where the domain of each variable can be restricted arbitrarily. A dichotomy is known for conservative CSP: for every fixed language Γ, c-CSP(Γ) is either in P or NP-complete. However, the characterization of conservatively tractable languages is of algebraic nature and the naive recognition algorithm is super-exponential in the domain size. The main contribution of this paper is a
more » ... omial-time algorithm that, given a constraint language Γ as input, decides if c-CSP(Γ) is tractable. In addition, if Γ is proven tractable the algorithm also outputs its coloured graph, which contains valuable information on the structure of Γ.
arXiv:1604.07063v2 fatcat:2vfuj6k755co3jylqd6n6qkjpm

The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable [chapter]

Clément Carbonnel
2016 Lecture Notes in Computer Science  
doi:10.1007/978-3-319-44953-1_9 fatcat:po7l4shprjgadgtf4vdcjcpxca

On the Kernelization of Global Constraints

Clément Carbonnel, Emmanuel Hebrard
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
In [Carbonnel and Hebrard, 2016] , a novel family of kernels, called loss-less kernels, was introduced for subset minimization problems.  ...  In this paper, we propose a definition of loss-less kernelization relevant to general constraints, hence less restrictive than the one in [Carbonnel and Hebrard, 2016] .  ... 
doi:10.24963/ijcai.2017/81 dblp:conf/ijcai/CarbonnelH17 fatcat:sydskmscbjfaffcpieokmvkq6i

Propagation via Kernelization: The Vertex Cover Constraint [chapter]

Clément Carbonnel, Emmanuel Hebrard
2016 Lecture Notes in Computer Science  
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method also provides a wealth of information to reason about in the context of constraint programming. We study the use of kernelization for designing propagators through the example of the Vertex Cover constraint. Since the classic kernelization rules often
more » ... to dominance rather than consistency, we introduce the notion of "loss-less" kernel. While our preliminary experimental results show the potential of the approach, they also show some of its limits. In particular, this method is more effective for vertex covers of large and sparse graphs, as they tend to have, relatively, smaller kernels.
doi:10.1007/978-3-319-44953-1_10 fatcat:bhsywgxelrgqthwlk7or2gsomi

On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

Clément Carbonnel, David A. Cohen, Martin C. Cooper, Stanislav Živný
2018 Algorithmica  
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. 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
more » ... generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.
doi:10.1007/s00453-018-0498-2 pmid:31007327 pmcid:PMC6449328 fatcat:hexfkxyuh5awngv76xkzamhqze

Partial Queries for Constraint Acquisition [article]

Christian Bessiere, Clement Carbonnel, Anton Dries, Emmanuel Hebrard, George Katsirelos, Nadjib Lazaar, Nina Narodytska, Claude-Guy Quimper, Kostas Stergiou, Dimosthenis C. Tsouros, Toby Walsh
2021 arXiv   pre-print
Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, we learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm, called QUACQ, that, given a negative example, focuses onto a constraint of the target network in a number of queries logarithmic in the size of the example. The whole
more » ... aint network can then be learned with a polynomial number of partial queries. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases.
arXiv:2003.06649v2 fatcat:m3az7xbfdjal7p6sfnd4lzxkpq

The Complexity of General-Valued CSPs Seen from the Other Side

Clement Carbonnel, Miguel Romero, Stanislav Zivny
2018 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)  
The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithm (unconditionally) as bounded treewidth modulo homomorphic
more » ... nce. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the k-th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.
doi:10.1109/focs.2018.00031 dblp:conf/focs/Carbonnel0Z18 fatcat:thbmrv7vgjhubawdkeg2fxwr54

A Simon-like effect in Go/No-Go tasks performed in isolation

Karen Davranche, Laurence Carbonnell, Clément Belletier, Franck Vidal, Pascal Huguet, Thibault Gajdos, Thierry Hasbroucq
2018 Psychonomic Bulletin & Review  
It is notably larger for incongruent than for congruent conditions (Carbonnell et al., 2013) .  ... 
doi:10.3758/s13423-018-1534-6 pmid:30284116 fatcat:y5sfhtd4gvfjhm7m7vd372lgoe

The complexity of general-valued CSPs seen from the other side [article]

Clement Carbonnel, Miguel Romero, Stanislav Zivny
2021 arXiv   pre-print
The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic
more » ... ence. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the k-th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.
arXiv:1710.03148v3 fatcat:d3hjvmkpyffmxebvafydgtrvfq

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
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. 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
more » ... generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.
arXiv:1704.06215v4 fatcat:q4bwigjw5jashh3beedms63lwa

Q-Intersection Algorithms for Constraint-Based Robust Parameter Estimation

Clement Carbonnel, Gilles Trombettoni, Philippe Vismara, Gilles Chabert
2014 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Given a set of axis-parallel n-dimensional boxes, the q-intersection is defined as the smallest box encompassing all the points that belong to at least q boxes. Computing the q-intersection is a combinatorial problem that allows us to handle robust parameter estimation with a numerical constraint programming approach. The q-intersection can be viewed as a filtering operator for soft constraints that model measurements subject to outliers. This paper highlights the equivalence of this operator
more » ... th the search of q-cliques in a graph whose boxicity is bounded by the number of variables in the constraint network. We present a computational study of the q-intersection. We also propose a fast heuristic and a sophisticated exact q-intersection algorithm. First experiments show that our exact algorithm outperforms the existing one while our heuristic performs an efficient filtering on hard problems.
doi:10.1609/aaai.v28i1.9117 fatcat:fpf23afbcrfitldqwlc54e4434
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