Tractability beyond β-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 β-acyclic. Despite the importance of many of these problems, there has been little success in generalizing these results beyond acyclicity....
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| Format: | Journal article |
| Language: | English |
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Elsevier
2022
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| Summary: | 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.
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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. |
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