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We extend the knowledge about so-called structural restrictions of #SAT by giving a polynomial time algorithm for β-acyclic #SAT. In contrast to previous algorithms in the area, our algorithm does not proceed by dynamic programming but works along an elimination order, solving a weighted version of constraint satisfaction. Moreover, we give evidence that… (More)

It is known that the data complexity of a Conjunctive Query (CQ) is determined only by the way its variables are shared between atoms, reflected by its hypergraph. In particular, Yannakakis [18, 3] proved that a CQ is decidable in linear time when it is α-acyclic, i.e. its hypergraph is α-acyclic; Bagan et al. [2] even state: Any CQ is decidable in linear… (More)

We extend the knowledge about so-called structural restrictions of #SAT by giving a polynomial time algorithm for β-acyclic #SAT. In contrast to previous algorithms in the area, our algorithm does not proceed by dynamic programming but works along an elimination order, solving a weighted version of constraint satisfaction. Moreover, we give evidence that… (More)

The notion of graph acyclicity has been extended to several notions of hypergraph acyclicity. In increasing order of generality: <i>gamma</i> acyclicity, <i>beta</i> acyclicity, and <i>alpha</i> acyclicity have met a great interest in many fields.
For each notion, we prove the equivalence between the numerous characterizations with a new, simpler proof, in… (More)

- Johann Brault-Baron, Lsv, Ens, Cachan, Inria
- 2014

The notion of graph acyclicity has been extended to several different notions of hypergraph acyclicity, in increasing order of generality: gamma acyclicity, beta acyclicity, and alpha acyclicity, that have met a great interest in many fields. We prove the equivalence between the numerous characterizations of each notion with a new, simpler proof, in a… (More)

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