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Approximation and Semantic Tree-Width of Conjunctive Regular Path Queries

Authors Diego Figueira , Rémi Morvan

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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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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'.

Cite As Get BibTex

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

Author Details

Diego Figueira
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR5800, F-33400 Talence, France
Rémi Morvan
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR5800, F-33400 Talence, France

References

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