Résumé
In this report, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called Tuple-Generating Dependencies or Datalog+/- rules). Our contribution is twofold. First, we introduce the class of \emph{greedy bounded treewidth sets} \emph{(gbts)} of rules, which covers guarded rules, and their known generalizations, namely (weakly) frontier-guarded rules. We provide a generic algorithm for query entailment with \emph{gbts}, which is worst-case optimal for combined complexity with bounded predicate arity, as well as for data complexity. Secondly, we classify several \emph{gbts} classes, whose complexity was unknown, namely frontier-one, frontier-guarded and weakly frontier-guarded rules, with respect to combined complexity (with both unbounded and bounded predicate arity) and data complexity.