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Documents authored by Carbonnel, Clément

Document
DOI: 10.4230/LIPIcs.CP.2022.9
Complexity of Minimum-Size Arc-Inconsistency Explanations

Authors: Christian Bessiere, Clément Carbonnel, Martin C. Cooper, and Emmanuel Hebrard

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract
Explaining the outcome of programs has become one of the main concerns in AI research. In constraint programming, a user may want the system to explain why a given variable assignment is not feasible or how it came to the conclusion that the problem does not have any solution. One solution to the latter is to return to the user a sequence of simple reasoning steps that lead to inconsistency. Arc consistency is a well-known form of reasoning that can be understood by a human. We consider explanations as sequences of propagation steps of a constraint on a variable (i.e. the ubiquitous revise function in arc consistency algorithms) that lead to inconsistency. We characterize, on binary CSPs, cases for which providing a shortest such explanation is easy: when domains are Boolean or when variables have maximum degree two. However, these polynomial cases are tight. Providing a shortest explanation is NP-hard if the maximum degree is three, even if the number of variables is bounded, or if domain size is bounded by three. It remains NP-hard on trees, despite the fact that arc consistency is a decision procedure on trees. Finally, the problem is not FPT-approximable unless the Gap-ETH is false.
Cite as

Christian Bessiere, Clément Carbonnel, Martin C. Cooper, and Emmanuel Hebrard. Complexity of Minimum-Size Arc-Inconsistency Explanations. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bessiere_et_al:LIPIcs.CP.2022.9,
  author =	{Bessiere, Christian and Carbonnel, Cl\'{e}ment and Cooper, Martin C. and Hebrard, Emmanuel},
  title =	{{Complexity of Minimum-Size Arc-Inconsistency Explanations}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.9},
  URN =		{urn:nbn:de:0030-drops-166380},
  doi =		{10.4230/LIPIcs.CP.2022.9},
  annote =	{Keywords: Constraint programming, constraint propagation, minimum explanations, complexity}
}
Document
DOI: 10.4230/LIPIcs.CP.2022.11
On Redundancy in Constraint Satisfaction Problems

Authors: Clément Carbonnel

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract
A constraint language Γ has non-redundancy f(n) if every instance of CSP(Γ) with n variables contains at most f(n) non-redundant constraints. If Γ has maximum arity r then it has non-redundancy O(n^r), but there are notable examples for which this upper bound is far from the best possible. In general, the non-redundancy of constraint languages is poorly understood and little is known beyond the trivial bounds Ω(n) and O(n^r). In this paper, we introduce an elementary algebraic framework dedicated to the analysis of the non-redundancy of constraint languages. This framework relates redundancy-preserving reductions between constraint languages to closure operators known as pattern partial polymorphisms, which can be interpreted as generic mechanisms to generate redundant constraints in CSP instances. We illustrate the power of this framework by deriving a simple characterisation of all languages of arity r having non-redundancy Θ(n^r).
Cite as

Clément Carbonnel. On Redundancy in Constraint Satisfaction Problems. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{carbonnel:LIPIcs.CP.2022.11,
  author =	{Carbonnel, Cl\'{e}ment},
  title =	{{On Redundancy in Constraint Satisfaction Problems}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.11},
  URN =		{urn:nbn:de:0030-drops-166409},
  doi =		{10.4230/LIPIcs.CP.2022.11},
  annote =	{Keywords: Constraint satisfaction problem, redundancy, universal algebra, extremal combinatorics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.19
On Singleton Arc Consistency for CSPs Defined by Monotone Patterns

Authors: Clément Carbonnel, David A. Cohen, Martin C. Cooper, and Stanislav Zivny

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
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 which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant progress towards a complete classification.
Cite as

Clément Carbonnel, David A. Cohen, Martin C. Cooper, and Stanislav Zivny. On Singleton Arc Consistency for CSPs Defined by Monotone Patterns. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{carbonnel_et_al:LIPIcs.STACS.2018.19,
  author =	{Carbonnel, Cl\'{e}ment and Cohen, David A. and Cooper, Martin C. and Zivny, Stanislav},
  title =	{{On Singleton Arc Consistency for CSPs Defined by Monotone Patterns}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.19},
  URN =		{urn:nbn:de:0030-drops-84876},
  doi =		{10.4230/LIPIcs.STACS.2018.19},
  annote =	{Keywords: constraint satisfaction problems, forbidden patterns, singleton arc consistency}
}
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