Temporal Valued Constraint Satisfaction Problems - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Temporal Valued Constraint Satisfaction Problems

Résumé

We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain Q that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint satisfaction problem: a relational structure is preserved by all order-preserving bijections if and only if all its relations have a first-order definition in (Q; <), and the CSPs for such structures are called temporal CSPs. Many optimization problems that have been studied intensively in the literature can be phrased as a temporal VCSP. We prove that a temporal VCSP is in P, or NP-complete. Our analysis uses the concept of fractional polymorphisms; this is the first dichotomy result for VCSPs over infinite domains which is complete in the sense that it treats all valued structures with a given automorphism group.

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Dates et versions

hal-04745208 , version 1 (20-10-2024)

Identifiants

  • HAL Id : hal-04745208 , version 1

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Manuel Bodirsky, Édouard Bonnet, Žaneta Semanišinová. Temporal Valued Constraint Satisfaction Problems. 2024. ⟨hal-04745208⟩
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