Fine-Grained Complexity Analysis of Queries: From Decision to Counting and Enumeration

Durand, Arnaud

doi:10.1145/3375395.3389130

Cited by 10 publications

(5 citation statements)

References 77 publications

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“…Similar dichotomies have been pursued by later works in more general settings, by allowing updates on the database [11], unions of queries [17], or functional dependencies [18]. Multiple surveys exist on this topic [10,32,75]. If we require a specific order on the output, then the more demanding task of ranked enumeration requires logarithmic delay, which is unavoidable [29] assuming the 𝑋 + 𝑌 conjecture [16].…”

Section: Related Workmentioning

confidence: 83%

Beyond Equi-joins: Ranking, Enumeration and Factorization

Tziavelis,

Gatterbauer,

Riedewald

2021

Preprint

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We study full acyclic join queries with general join predicates that involve conjunctions and disjunctions of inequalities, focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking function. Our approach offers strong time and space complexity guarantees in the standard RAM model of computation, getting surprisingly close to those of equi-joins. With 𝑛 denoting the number of tuples in the database, we guarantee that for every value of 𝑘, the 𝑘 top-ranked answers are returned in O (𝑛 polylog 𝑛 +𝑘 log 𝑘) time and O (𝑛 polylog 𝑛 +𝑘) space. This is within a polylogarithmic factor of the best-known guarantee for equi-joins and even O (𝑛 + 𝑘), the time it takes to look at the input and output 𝑘 answers. The key ingredient is an O (𝑛 polylog 𝑛)-size factorized representation of the query output, which is constructed on-the-fly for a given query and database. As a side benefit, our techniques are also applicable to unranked enumeration (where answers can be returned in any order) for joins with inequalities, returning 𝑘 answers in O (𝑛 polylog 𝑛 + 𝑘). This guarantee improves over the state of the art for large values of 𝑘. In an experimental study, we show that our ranked-enumeration approach is not only theoretically interesting, but also fast and memory-efficient in practice.

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Section: Related Workmentioning

confidence: 83%

Beyond Equi-joins: Ranking, Enumeration and Factorization

Tziavelis,

Gatterbauer,

Riedewald

2021

Preprint

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show abstract

“…In Section 5.2, we will give more details on handling free-connex CQs for the task of ranked enumeration. For an in-depth explanation of the above dichotomy, we refer the reader to recent tutorials on the topic [21,54].…”

Section: Known Results On Unranked and Lexicographic Enumerationmentioning

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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“…Similar as it sounds, pattern searching on a relational event graph is drastically different from Problem 1 and 2 such that there is little overlap -in neither results nor techniques -between our solutions and those in [6,14,15]. Delay minimization is an important topic in the literature of joins and conjunctive queries; see [5,9,12,13,[20][21][22][23]34,35,41,[43][44][45] and their references. Regarding our problems, we are not aware of previous work giving a result better than what has already been mentioned.…”

Section: Related Workmentioning

confidence: 99%

Space-Query Tradeoffs in Range Subgraph Counting and Listing

Deng¹,

Lu²,

Tao³

2023

Preprint

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This paper initializes the study of range subgraph counting and range subgraph listing, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as opposed to all, vertices. In the first problem, there is an undirected graph G where each vertex carries a real-valued attribute. Given an interval q and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced by the vertices whose attributes fall in q. The second problem has the same setup except that a query needs to enumerate (rather than count) those occurrences with a small delay. In both problems, our goal is to understand the tradeoff between space usage and query cost, or more specifically: (i) given a target on query efficiency, how much pre-computed information about G must we store? (ii) Or conversely, given a budget on space usage, what is the best query time we can hope for? We establish a suite of upper-and lower-bound results on such tradeoffs for various query patterns.

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Fine-Grained Complexity Analysis of Queries: From Decision to Counting and Enumeration

Cited by 10 publications

References 77 publications

Beyond Equi-joins: Ranking, Enumeration and Factorization

Beyond Equi-joins: Ranking, Enumeration and Factorization

Any-k Algorithms for Enumerating Ranked Answers to Conjunctive Queries

Space-Query Tradeoffs in Range Subgraph Counting and Listing

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