Tractability beyond β-acyclicity for conjunctive queries with negation and SAT

Abstract

Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is β-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 β-acyclicity. We demonstrate that nest-set width has desirable properties and algorithmic significance. In particular, evaluation of boolean conjunctive queries with negation (CQ¬) is tractable for classes with bounded nest-set width. Furthermore, propositional satisfiability (SAT) is fixed-parameter tractable when parameterized by nest-set width.