When is the evaluation of conjunctive queries tractable?

@inproceedings{Grohe2001WhenIT,
  title={When is the evaluation of conjunctive queries tractable?},
  author={Martin Grohe and Thomas Schwentick and Luc Segoufin},
  booktitle={STOC},
  year={2001}
}
The evaluation of conjunctive queries is hard both with respect to its combined complexity (NP-complete) and its parameterized complexity (W[1]-complete). It becomes tractable (PTIME for combined complexity, FPT for parameterized complexity), when the underlying graphs of the conjunctive queries have bounded tree-width [2]. We show that, in some sense, this is optimal both with respect to combined and parameterized complexity: For every class C of graphs, the evaluation of all conjunctive… CONTINUE READING
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