Tractability beyond -acyclicity for conjunctive queries with negation and SAT

Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is /3-acyclic. Despite the importance of many of these problems, there has been little success in generalizing these results beyond acyclicity. In this paper, we take on this challenge and propose nest-set width, a novel generalization of hypergraph /3-acyclicity. We demonstrate that nest-set width has desirable properties and algorithmic significance. In particular, evaluation of boolean conjunctive queries with negation (CQ not sign ) is tractable for classes with bounded nest-set width. Furthermore, propositional satisfiability (SAT) is fixed-parameter tractable when parameterized by nestset width. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).