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Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability

Authors Antoine Amarilli , Timothy van Bremen , Kuldeep S. Meel

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Author Details

Antoine Amarilli
  • LTCI, Télécom Paris, Institut Polytechnique de Paris, France
Timothy van Bremen
  • National University of Singapore, Singapore
Kuldeep S. Meel
  • University of Toronto, Canada

Funding

This project was supported in part by the National Research Foundation Singapore under its NRF Fellowship programme [NRF-NRFFAI1-2019-0004] and Campus for Research Excellence and Technological Enterprise (CREATE) programme, as well as the Ministry of Education Singapore Tier 1 and 2 grants R-252-000-B59-114 and MOE-T2EP20121-0011. Amarilli was partially supported by the ANR project EQUUS ANR-19-CE48-0019, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 431183758, and by the ANR project ANR-18-CE23-0003-02 ("CQFD"). This work was done in part while Amarilli was visiting the Simons Institute for the Theory of Computing.

Acknowledgements

The authors thank Octave Gaspard for pointing out some oversights in some proofs, which are corrected in the present version.

Cite AsGet BibTex

Antoine Amarilli, Timothy van Bremen, and Kuldeep S. Meel. Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICDT.2024.15

Abstract

Query evaluation over probabilistic databases is a notoriously intractable problem - not only in combined complexity, but for many natural queries in data complexity as well [Antoine Amarilli et al., 2017; Nilesh N. Dalvi and Dan Suciu, 2012]. This motivates the study of probabilistic query evaluation through the lens of approximation algorithms, and particularly of combined FPRASes, whose runtime is polynomial in both the query and instance size. In this paper, we focus on tuple-independent probabilistic databases over binary signatures, which can be equivalently viewed as probabilistic graphs. We study in which cases we can devise combined FPRASes for probabilistic query evaluation in this setting. We settle the complexity of this problem for a variety of query and instance classes, by proving both approximability and (conditional) inapproximability results. This allows us to deduce many corollaries of possible independent interest. For example, we show how the results of [Marcelo Arenas et al., 2021] on counting fixed-length strings accepted by an NFA imply the existence of an FPRAS for the two-terminal network reliability problem on directed acyclic graphs: this was an open problem until now [Rico Zenklusen and Marco Laumanns, 2011]. We also show that one cannot extend a recent result [Timothy van Bremen and Kuldeep S. Meel, 2023] that gives a combined FPRAS for self-join-free conjunctive queries of bounded hypertree width on probabilistic databases: neither the bounded-hypertree-width condition nor the self-join-freeness hypothesis can be relaxed. Finally, we complement all our inapproximability results with unconditional lower bounds, showing that DNNF provenance circuits must have at least moderately exponential size in combined complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query processing and optimization (theory)
Keywords
  • Probabilistic query evaluation
  • tuple-independent databases
  • approximation

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