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arXiv · 2007.08876

Tractability Beyond $\beta$-Acyclicity for Conjunctive Queries with Negation

Matthias Lanzinger
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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 $\beta$-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 $\beta$-acyclicity. We demonstrate that nest-set width has desirable properties and algorithmic significance. In particular, evaluation of boolean conjunctive queries with negation is tractable for classes with bounded nest-set width. Furthermore, propositional satisfiability is fixed-parameter tractable when parameterized by nest-set width.

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Matthias Lanzinger. 2020-07-17. Tractability Beyond $\beta$-Acyclicity for Conjunctive Queries with Negation. https://doi.org/10.1145/3452021.3458308

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