Generic multiset programming with discrimination-based joins and symbolic Cartesian products

Henglein, Fritz; Larsen, Ken Friis

doi:10.1007/s10990-011-9078-8

Cited by 9 publications

(7 citation statements)

References 25 publications

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“…Products of unions of singletons are studied under different names (rectangles, bicliques in binary relations, n-sets, formal concepts) and several representation systems are based on unions of products of unions of singletons, such as generalised disjunctive normal forms (GDNFs) studied as succinct presentations of inputs to CSPs [Chen and Grohe 2010], tilings of databases by bicliques, and n-sets or formal concepts [Geerts et al 2004;Cerf et al 2009]. The lazy, symbolic representation of the Cartesian product of two sets, which is used by factorised representations to avoid eager materialisation of all pairs of elements from the two sets, has also been recently used in the design of the GMP functional programming library for SQL-like processing on multisets [Henglein and Larsen 2010].…”

Section: Related Workmentioning

confidence: 99%

Size Bounds for Factorised Representations of Query Results

Olteanu

Závodný

2015

ACM Trans. Database Syst.

109

156

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We study two succinct representation systems for relational data based on relational algebra expressions with unions, Cartesian products, and singleton relations: f-representations, which employ algebraic factorisation using distributivity of product over union, and d-representations, which are f-representations where further succinctness is brought by explicit sharing of repeated subexpressions.In particular we study such representations for results of conjunctive queries. We derive tight asymptotic bounds for representation sizes and present algorithms to compute representations within these bounds. We compare the succinctness of f-representations and d-representations for results of equi-join queries, and relate them to fractional edge covers and fractional hypertree decompositions of the query hypergraph.Recent work showed that f-representations can significantly boost the performance of query evaluation in centralised and distributed settings and of machine learning tasks. ACM Reference Format:Dan Olteanu and Jakub Závodný. 2015. Size bounds for factorised representations of query results. ACM Trans.

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Section: Related Workmentioning

confidence: 99%

Size Bounds for Factorised Representations of Query Results

Olteanu

Závodný

2015

ACM Trans. Database Syst.

109

156

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“…When the predicates and comparisons are more expensive, such as on unbounded strings, then one needs something like discrimination-based techniques [Henglein and Larsen 2010] in order to retain the linear time guarantee.…”

Section: (×)mentioning

confidence: 99%

“…Bag (λp → e) e ′ | q = { functors over comprehension (10) } (λp → e) e ′ | q 8.6 Joins Join order optimization is one of the most powerful optimization techniques, even though it is known to be insufficient for generating worst-case optimal join implementations [Ngo et al 2012]. It can be shown that extending merge from binary to n-ary functions, combined with the generic trie implementation of ix based on (15a)ś(15d) [Henglein and Hinze 2013] and symbolic Cartesian product constructors, yields worst-case optimal joins that dramatically outperform conventional query processors on cyclic join queries, specifically triangle queries, also in practice [Henglein and Larsen 2010]. Cartesian product and equijoin are associative and commutative (up to canonical isomorphisms), and so queries involving two or more joins offer many opportunities for rearranging the query in order to improve performance.…”

Section: Comprehensionsmentioning

confidence: 99%

Relational algebra by way of adjunctions

Gibbons

Henglein

Hinze

et al. 2018

Proc. ACM Program. Lang.

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Bulk types such as sets, bags, and lists are monads, and therefore support a notation for database queries based on comprehensions. This fact is the basis of much work on database query languages. The monadic structure easily explains most of standard relational algebraÐspecifically, selections and projectionsÐallowing for an elegant mathematical foundation for those aspects of database query language design. Most, but not all: monads do not immediately offer an explanation of relational join or grouping, and hence important foundations for those crucial aspects of relational algebra are missing. The best they can offer is cartesian product followed by selection. Adjunctions come to the rescue: like any monad, bulk types also arise from certain adjunctions; we show that by paying due attention to other important adjunctions, we can elegantly explain the rest of standard relational algebra. In particular, graded monads provide a mathematical foundation for indexing and grouping, which leads directly to an efficient implementation, even of joins.

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“…If executed as a query, the interpreter generates a single (statically defined) SQL query that can take advantage of the database's indexing or other query optimisation; if executed in-memory, the expression will by default be interpreted as a quadratic nested loop. (Efficient in-memory implementations of query expressions are also possible [16]. )…”

Section: (Name=xname)]mentioning

confidence: 99%

Effective quotation

Cheney

Lindley

Radanne

et al. 2014

Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation

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Language-integrated query techniques have been explored in a number of different language designs. We consider two different, type-safe approaches employed by Links and F#. Both approaches provide rich dynamic query generation capabilities, and thus amount to a form of heterogeneous staged computation, but to date there has been no formal investigation of their relative expressiveness. We present two core calculi Eff and Quot, respectively capturing the essential aspects of language-integrated querying using effects in Links and quotation in LINQ. We show via translations from Eff to Quot and back that the two approaches are equivalent in expressiveness. Based on the translation from Eff to Quot, we extend a simple Links compiler to handle queries.

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Generic multiset programming with discrimination-based joins and symbolic Cartesian products

Cited by 9 publications

References 25 publications

Size Bounds for Factorised Representations of Query Results

Size Bounds for Factorised Representations of Query Results

Relational algebra by way of adjunctions

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