Point-width and Max-CSPs

Clement Carbonnel (1) , Miguel Romero (2) , Stanislav Živný (3)

1 COCONUT - Agents, Apprentissage, Contraintes
2 Universidad Adolfo Ibáñez [Santiago]
3 University of Oxford

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 MIM-width and β-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.

Domaines: Complexité [cs.CC]

Clement Carbonnel, Miguel Romero, Stanislav Živný. Point-width and Max-CSPs. LICS 2019 - 34th ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. pp.1-13, ⟨10.1109/LICS.2019.8785660⟩. ⟨hal-02088817⟩