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Antoine Mottet

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5 papers
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5

MFCS Conference 2024 Conference Paper

Generalized Completion Problems with Forbidden Tournaments

  • Zeno Bitter
  • Antoine Mottet

A recent result by Bodirsky and Guzmán-Pro gives a complexity dichotomy for the following class of computational problems, parametrized by a finite family F of finite tournaments: given an undirected graph, does there exist an orientation of the graph that avoids every tournament in F? One can see the edges of the input graphs as constraints imposing to find an orientation. In this paper, we consider a more general version of this problem where the constraints in the input are not necessarily about pairs of variables and impose local constraints on the global oriented graph to be found. Our main result is a complexity dichotomy for such problems, as well as a classification of such problems where the yes-instances have bounded treewidth duality. As a consequence, we obtain a streamlined proof of the result by Bodirsky and Guzmán-Pro using the theory of smooth approximations due to Mottet and Pinsker.

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CSL Conference 2024 Conference Paper

Promise and Infinite-Domain Constraint Satisfaction

  • Antoine Mottet

Two particularly active branches of research in constraint satisfaction are the study of promise constraint satisfaction problems (PCSPs) with finite templates and the study of infinite-domain constraint satisfaction problems with ω-categorical templates. In this paper, we explore some connections between these two hitherto unrelated fields and describe a general approach to studying the complexity of PCSPs by constructing suitable infinite CSP templates. As a result, we obtain new characterizations of the power of various classes of algorithms for PCSPs, such as first-order logic, arc consistency reductions, and obtain new proofs of the characterizations of the power of the classical linear and affine relaxations for PCSPs.

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IJCAI Conference 2018 Conference Paper

Classification Transfer for Qualitative Reasoning Problems

  • Manuel Bodirsky
  • Peter Jonsson
  • Barnaby Martin
  • Antoine Mottet

We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use of primitive positive (pp) interpretations and pp-homotopy. We demonstrate the methodology by giving a full complexity classification of all constraint languages that are first-order definable in Allen's Interval Algebra and contain the basic relations (s) and (f). In the case of the Rectangle Algebra we answer in the affirmative the old open question as to whether ORD-Horn is a maximally tractable subset among the (disjunctive, binary) relations. We then generalise our results for the Rectangle Algebra to the r-dimensional Block Algebra.

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I&C Journal 2016 Journal Article

Distance constraint satisfaction problems

  • Manuel Bodirsky
  • Victor Dalmau
  • Barnaby Martin
  • Antoine Mottet
  • Michael Pinsker

We study the complexity of constraint satisfaction problems for templates Γ over the integers where the relations are first-order definable from the successor function. In the case that Γ is locally finite (i. e. , the Gaifman graph of Γ has finite degree), we show that Γ is homomorphically equivalent to a structure with one of two classes of polymorphisms (which we call modular max and modular min) and the CSP for Γ can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or the CSP for Γ is NP-complete. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), this proves that those CSPs have a complexity dichotomy, that is, are either in P or NP-complete.

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v2026.09.13