Tractable Orders for Direct Access to Ranked Answers of Conjunctive Queries

Carmeli, Nofar; Tziavelis, Nikolaos; Gatterbauer, Wolfgang; Kimelfeld, Benny; Riedewald, Mirek

doi:10.1145/3452021.3458331

Cited by 10 publications

(6 citation statements)

References 34 publications

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“…Further investigation of the speciic orders that can be eiciently achieved goes beyond the scope of this work, and indeed it was carried out following the publication of the conference version of this article. Carmeli et al [14] characterized the orders that can be achieved with logarithmic access time after linear preprocessing. They explained that the order we achieve here is lexicographical, and built upon our random-access algorithm for CQs to design an improved algorithm that supports any tractable lexicographic order speciied by the user.…”

Section: Discussionmentioning

confidence: 99%

“…In turn, this implies that there is an ordering < of the UCQ's free variables ì that does not have a disruptive trio (cf. [14]) with respect to any CQ . Using results of (Section 3 of) [14], we then obtain RAccess⟨lin, log⟩-algorithms A for for all ∅ ≠ ⊆ [1, ] that also provide inverted access in logarithmic time and that, moreover, are compatible in the sense that they enumerate the query's result tuples in the same lexicographic order, namely the lexicographic order induced by the ordering < of the UCQ's free variables ì .…”

Section: Ucqs That Allow For Random-accessmentioning

confidence: 99%

“…[14]) with respect to any CQ . Using results of (Section 3 of) [14], we then obtain RAccess⟨lin, log⟩-algorithms A for for all ∅ ≠ ⊆ [1, ] that also provide inverted access in logarithmic time and that, moreover, are compatible in the sense that they enumerate the query's result tuples in the same lexicographic order, namely the lexicographic order induced by the ordering < of the UCQ's free variables ì . This proves that the UCQ is indeed an mc-UCQ, provided that the CQ ′ is -acyclic.…”

Section: Ucqs That Allow For Random-accessmentioning

confidence: 99%

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Answering (Unions of) Conjunctive Queries using Random Access and Random-Order Enumeration

Carmeli

Zeevi

Berkholz

et al. 2022

ACM Trans. Database Syst.

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As data analytics becomes more crucial to digital systems, so grows the importance of characterizing the database queries that admit a more efficient evaluation. We consider the tractability yardstick of answer enumeration with a polylogarithmic delay after a linear-time preprocessing phase. Such an evaluation is obtained by constructing, in the preprocessing phase, a data structure that supports polylogarithmic-delay enumeration. In this article, we seek a structure that supports the more demanding task of a “random permutation”: polylogarithmic-delay enumeration in truly random order. Enumeration of this kind is required if downstream applications assume that the intermediate results are representative of the whole result set in a statistically meaningful manner. An even more demanding task is that of “random access”: polylogarithmic-time retrieval of an answer whose position is given. We establish that the free-connex acyclic CQs are tractable in all three senses: enumeration, random-order enumeration, and random access; and in the absence of self-joins, it follows from past results that every other CQ is intractable by each of the three (under some fine-grained complexity assumptions). However, the three yardsticks are separated in the case of a union of CQs (UCQ): while a union of free-connex acyclic CQs has a tractable enumeration, it may (provably) admit no random access. We identify a fragment of such UCQs where we can guarantee random access with polylogarithmic access time (and linear-time preprocessing) and a more general fragment where we can guarantee tractable random permutation. For general unions of free-connex acyclic CQs, we devise two algorithms with relaxed guarantees: one has logarithmic delay in expectation, and the other provides a permutation that is almost uniformly distributed. Finally, we present an implementation and an empirical study that show a considerable practical superiority of our random-order enumeration approach over state-of-the-art alternatives.

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Section: Discussionmentioning

confidence: 99%

Section: Ucqs That Allow For Random-accessmentioning

confidence: 99%

Section: Ucqs That Allow For Random-accessmentioning

confidence: 99%

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Answering (Unions of) Conjunctive Queries using Random Access and Random-Order Enumeration

Carmeli

Zeevi

Berkholz

et al. 2022

ACM Trans. Database Syst.

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show abstract

“…Hardness hypotheses. Works in the wider area of enumeration [14,37,38,30] have used certain hypotheses on the hardness of algorithmic problems to prove lower bounds and achieve dichotomies for CQs. In this work, we extend some of these results to the case of ranked enumeration using the same set of hypotheses.…”

Section: Complexity Measures and Hypothesesmentioning

confidence: 99%

“…Our efficient encoding of the CQ answers as a (T-)DP instance with intermediate nodes in-between bicliques [59] can be interpreted as factorization [120], which has been studied systematically in the context of factorized databases [16,105,106]. The main idea is to represent the query answers compactly while supporting different types of tasks, such as enumeration [107,83], aggregation [2,3], learning models [113], uniform sampling [39] and directly accessing ranked answers [38]. Related to this line of work are different representation schemes [84] and the exploration of the continuum between representation size and enumeration delay [49].…”

Section: Related Workmentioning

confidence: 99%

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Tziavelis¹,

Gatterbauer²,

Riedewald³

2022

Preprint

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We study ranked enumeration for Conjunctive Queries (CQs) where the answers are ordered by a given ranking function (e.g., an ORDER BY clause in SQL). We develop "any-k" algorithms which, without knowing the number 𝑘 of desired answers, push the ranking into joins and avoid materializing the join output earlier than necessary. For this to be possible, the ranking function needs to obey a certain kind of monotonicity; the supported ranking functions include the common sum-of-weights case where query answers are compared by sums of input weights, as well as any commutative selective dioid. One core insight of our work is that the problem is closely related to the fundamental task of path enumeration in a weighted DAG. We generalize and improve upon classic research on finding the 𝑘 th shortest path and unify into the same framework several solutions from different areas that had been studied in isolation. For the time to the 𝑘 th ranked CQ answer (for every value of 𝑘), our approach is optimal in data complexity precisely for the same class of queries where unranked enumeration is optimal-and only slower by a logarithmic factor. In a more careful analysis of combined complexity, we uncover a previously unknown tradeoff between two different any-k algorithms: one has lower complexity when the number of returned results is small, the other when the number is very large. This tradeoff is eliminated under a stricter monotonicity property that we exploit to design a novel algorithm that asymptotically dominates all previously known alternatives, including the well-known algorithm of Eppstein for sum-of-weights path enumeration. We empirically demonstrate the findings of our theoretical analysis in an experimental study that highlights the superiority of our approach over the join-then-rank approach that existing database systems typically follow.

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The resilience of conjunctive queries with inequalities

Qin

Zhou

2022

Information Sciences

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Tractable Orders for Direct Access to Ranked Answers of Conjunctive Queries

Cited by 10 publications

References 34 publications

Answering (Unions of) Conjunctive Queries using Random Access and Random-Order Enumeration

Answering (Unions of) Conjunctive Queries using Random Access and Random-Order Enumeration

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

The resilience of conjunctive queries with inequalities

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