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Approximation and Semantic Tree-Width of Conjunctive Regular Path Queries
Authors
Diego Figueira 
,
Rémi Morvan
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26th International Conference on Database Theory (ICDT 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Database Theory (ICDT) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-03-17
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Diego Figueira and Rémi Morvan. Approximation and Semantic Tree-Width of Conjunctive Regular Path Queries. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICDT.2023.15
https://doi.org/10.4230/LIPIcs.ICDT.2023.15
Abstract
We show that the problem of whether a query is equivalent to a query of tree-width k is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barceló, Romero, and Vardi [Pablo Barceló et al., 2016] has shown decidability for the case k = 1, and here we show that decidability in fact holds for any arbitrary k > 1. The algorithm is in 2ExpSpace, but for the restricted but practically relevant case where all regular expressions of the query are of the form a^* or (a_1 + ... + a_n) we show that the complexity of the problem drops to Π^p_2.
We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number k, builds the maximal under-approximation of tree-width k of a UC2RPQ. The maximal under-approximation of tree-width k of a query q is a query q' of tree-width k which is contained in q in a maximal and unique way, that is, such that for every query q'' of tree-width k, if q'' is contained in q then q'' is also contained in q'.
Subject Classification
ACM Subject Classification
- Information systems → Query languages for non-relational engines
- Theory of computation → Parameterized complexity and exact algorithms
- Theory of computation → Database query processing and optimization (theory)
Keywords
- graph databases
- conjunctive regular path queries
- semantic optimization
- tree-width
- containment
- approximation
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References
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