When is approximate counting for conjunctive queries tractable?

Arenas, Marcelo; Croquevielle, Luis Alberto; Jayaram, Rajesh; Riveros, Cristian

doi:10.1145/3406325.3451014

Cited by 12 publications

(27 citation statements)

References 31 publications

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“…The equivalence of the width parameters in the case of bounded arity is well known; we provide an explicit argument in Observation 34. For completeness, we also compare our results to recent work of Arenas et al [3]. The lower bounds either rely on the assumption that NP = RP or on the rETH.…”

Section: Unbounded Aritymentioning

confidence: 68%

“…As others have noted [3,19] CQs are common in database systems. They are called selectproject-join queries in relational algebra and select-from-where queries in SQL.…”

Section: Introductionmentioning

confidence: 80%

“…As stated in Observation 10, there is little hope of improving Theorem 13 to obtain an FPRAS instead of an FPTRAS. However, as mentioned previously, if disequalities are not part of the query, the result by Arenas et al [3] also applies to classes of hypergraphs with unbounded arity -they give an FPRAS for #CQ (Φ C ) if C is a class of hypergraphs with bounded hypertreewidth. We improve this result by showing that it suffices to require bounded fractional hypertreewidth.…”

Section: Application To Locally Injective Homomorphismsmentioning

confidence: 85%

“…Interestingly, the situation changes if we consider CQs without extensions. Arenas, Croquevielle, Jayaram, and Riveros [3] give an FPRAS for #CQ (Φ C ) for any bounded-treewidth class C of hypergraphs. Their result will be stated formally as Theorem 38 in Section 5.2 (where it will be improved).…”

Section: Application To Locally Injective Homomorphismsmentioning

confidence: 99%

“…In Section 5.1 we extend Theorem 5 to this setting (in the case of #DCQ (Φ C )), obtaining a stronger result in terms of adaptive width. In Section 5.2 we improve the result of [3] which gives an FPRAS for #CQ (Φ C ) by bounding fractional hypertreewidth rather than hypertreewidth.…”

Section: Beyond Bounded Aritymentioning

confidence: 99%

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Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Focke¹,

Goldberg²,

Roth³

et al. 2021

Preprint

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We study the complexity of approximating the number of answers to a small query ϕ in a large database D. We establish an exhaustive classification into tractable and intractable cases if ϕ is a conjunctive query with disequalities and negations:• If there is a constant bound on the arity of ϕ, and if the randomised Exponential Time Hypothesis (rETH) holds, then the problem has a fixed-parameter tractable approximation scheme (FPTRAS) if and only if the treewidth of ϕ is bounded.• If the arity is unbounded and we allow disequalities only, then the problem has an FPTRAS if and only if the adaptive width of ϕ (a width measure strictly more general than treewidth) is bounded; the lower bound relies on the rETH as well.Additionally we show that our results cannot be strengthened to achieve a fully polynomial randomised approximation scheme (FPRAS): We observe that, unless NP = RP, there is no FPRAS even if the treewidth (and the adaptive width) is 1. However, if there are neither disequalities nor negations, we prove the existence of an FPRAS for queries of bounded fractional hypertreewidth, strictly generalising the recently established FPRAS for conjunctive queries with bounded hypertreewidth due to Arenas, Croquevielle, Jayaram and Riveros (STOC 2021).

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Section: Unbounded Aritymentioning

confidence: 68%

“…As others have noted [3,19] CQs are common in database systems. They are called selectproject-join queries in relational algebra and select-from-where queries in SQL.…”

Section: Introductionmentioning

confidence: 80%

Section: Application To Locally Injective Homomorphismsmentioning

confidence: 85%

Section: Application To Locally Injective Homomorphismsmentioning

confidence: 99%

Section: Beyond Bounded Aritymentioning

confidence: 99%

See 3 more Smart Citations

Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Focke¹,

Goldberg²,

Roth³

et al. 2021

Preprint

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Exact and Approximate Pattern Counting in Degenerate Graphs: New Algorithms, Hardness Results, and Complexity Dichotomies

Bressan

Roth

2022

2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

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Uniform Operational Consistent Query Answering

Livshits

Pieris

Schneider

2022

Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there are efficient approximations for computing the percentage of repairs, as well as of sequences of operations leading to repairs, that entail a given query when we focus on primary keys, conjunctive queries, and assuming the query is fixed (i.e., in data complexity). However, it has been left open whether such approximations exist when the query is part of the input (i.e., in combined complexity). We show that this is the case when we focus on self-join-free conjunctive queries of bounded generelized hypertreewidth. We also show that it is unlikely that efficient approximation schemes exist once we give up one of the adopted syntactic restrictions, i.e., self-join-freeness or bounding the generelized hypertreewidth. Towards the desired approximation schemes, we introduce a novel counting complexity class, called SpanTL, show that each problem in SpanTL admits an efficient approximation scheme by using a recent approximability result in the context of tree automata, and then place the problems of interest in SpanTL. CCS CONCEPTS• Information systems → Data management systems.

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When is approximate counting for conjunctive queries tractable?

Cited by 12 publications

References 31 publications

Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations

Exact and Approximate Pattern Counting in Degenerate Graphs: New Algorithms, Hardness Results, and Complexity Dichotomies

Uniform Operational Consistent Query Answering

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