On the equivalence and rewriting of aggregate queries

Grumbach, Stéphane; Rafanelli, Maurizio; Tininini, Leonardo

doi:10.1007/s00236-004-0101-y

Cited by 17 publications

(8 citation statements)

References 54 publications

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“…These characterizations were generalized in Cohen et al [1999] to aggregate queries with disjunctions. Equivalence of conjunctive queries with comparisons and the aggregation functions avg and percent was characterized in Grumbach et al [2004]. The equivalence problem for aggregate queries with negation, comparisons and arbitrary aggregation functions was studied in Cohen et al [2005] and classes of queries were identified for which the problem is decidable.…”

Section: Aggregate Query Equivalencementioning

confidence: 99%

“…The characterizations of equivalence from Nutt et al [1998] and Grumbach et al [2004], along with the decision procedure from , can be used in conjunction with the results of this article to find equivalent rewritings that are not isomorphic to the given query.…”

Section: Aggregate Query Equivalencementioning

confidence: 99%

“…The rewriting techniques of Cohen et al [1999Cohen et al [ , 2000aCohen et al [ , 2003, Grumbach and Tininini [2003], and Grumbach et al [2004], extend the work of Levy et al [1995a] to aggregate queries. Similarly to Levy et al [1995a], they are based on characterizations for aggregate-query equivalence.…”

Section: Rewriting Aggregate Queriesmentioning

confidence: 99%

“…In Grumbach and Tininini [2003], only the aggregation functions count, sum, prod, avg and percent (with views and queries defined over a single relation) were considered. In Grumbach et al [2004], rewriting countqueries was considered. In this work, isomorphism modulo a product was used in combination with complex arithmetical computations to recover count values from the views.…”

Section: Rewriting Aggregate Queriesmentioning

confidence: 99%

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Rewriting queries with arbitrary aggregation functions using views

Cohen

Nutt

Sagiv

2006

ACM Trans. Database Syst.

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The problem of rewriting aggregate queries using views is studied for conjunctive queries with arbitrary aggregation functions and built-in predicates. Two types of queries over views are introduced for rewriting aggregate queries: pure candidates and aggregate candidates. Pure candidates can be used to rewrite arbitrary aggregate queries. Aggregate candidates can be used to rewrite queries containing aggregate functions definable in terms of a commutative-semigroup operation. For both types of candidates (as well as for several relaxations of these candidates), the unfolding property holds. This allows characterizations for query equivalence to be used to determine whether a candidate is a rewriting of a query. The complexity of the rewriting-existence problem is also studied and upper and lower complexity bounds are given.

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Section: Aggregate Query Equivalencementioning

confidence: 99%

Section: Aggregate Query Equivalencementioning

confidence: 99%

Section: Rewriting Aggregate Queriesmentioning

confidence: 99%

Section: Rewriting Aggregate Queriesmentioning

confidence: 99%

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Rewriting queries with arbitrary aggregation functions using views

Cohen

Nutt

Sagiv

2006

ACM Trans. Database Syst.

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“…Syntactic characterizations of equivalences among positive aggregate queries with the functions max, sum, and count have been given in Nutt et al [1998] and Cohen et al [1999]. These results have been extended in Grumbach et al [1999Grumbach et al [ , 2004 to positive conjunctive queries with the functions prod and avg. Thus, there are results on the equivalence problem for non-aggregate queries with negation as well as for aggregate queries without negation.…”

Section: Introductionmentioning

confidence: 99%

Equivalences among aggregate queries with negation

Cohen

Sagiv

Nutt³

2005

ACM Trans. Comput. Logic

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Query equivalence is investigated for disjunctive aggregate queries with negated subgoals, constants and comparisons. A full characterization of equivalence is given for the aggregation functions count, max, sum, prod, top2 and parity. A related problem is that of determining, for a given natural number N , whether two given queries are equivalent over all databases with at most N constants. This problem is called bounded equivalence. A complete characterization of decidability of bounded equivalence is given. In particular, it is shown that this problem is decidable for all the above aggregation functions as well as for cntd (count distinct) and avg. For quasilinear queries (i.e., queries in which predicates that occur positively are not repeated), it is shown that equivalence can be decided in polynomial time for the aggregation functions count, max, sum, parity, prod, top2 and avg. A similar result holds for cntd provided that a few additional conditions hold. The results are couched in terms of abstract characteristics of aggregation functions, and new proof techniques are used. Finally, the results above also imply that equivalence, under bag-set semantics, is decidable for nonaggregate queries with negation. • 329 • S. Cohen et al.quasilinear queries, equivalence boils down to isomorphism, which can be decided in polynomial time. AGGREGATION FUNCTIONSAn aggregate query is executed in two steps. First, data is collected from a database as specified by the nonaggregate part of the query. Then, the results are grouped into multisets (or bags), an aggregation function is applied to the multisets, and the aggregates are returned as answers.The queries that we consider in this article contain the aggregation functions count and cntd, which for a bag return the number of elements and distinct elements, respectively; parity, which returns 0 or 1, depending on whether the number of elements in the bag is even or odd; sum, prod and avg, which return the sum, product and average of the elements of a bag, respectively; max, which returns the maximum among the elements of a bag; and top2, which returns a pair consisting of the two greatest different elements of a bag.The reader will notice in the course of the article that our results for max and top2 immediately carry over to min and bot2, which select the minimum and the two least elements out of a multiset of numbers, respectively. Moreover, our results for top2 can easily be generalized to the function topK , which selects the K greatest different elements.Our arguments to prove decidability of equivalence for certain classes of aggregate queries rely on the fact that the aggregation functions take values in special kinds of abelian monoids and are defined in terms of the operations of those monoids. To make this formal, we will introduce the class of monoid aggregation functions and two of its subclasses. We will show that all of the above functions, except cntd, prod and avg, belong to one of these two subclasses. In general, an aggregation function maps multisets...

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Aggregation: Expressiveness and Containment

Cohen¹

2009

Encyclopedia of Database Systems

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On the equivalence and rewriting of aggregate queries

Cited by 17 publications

References 54 publications

Rewriting queries with arbitrary aggregation functions using views

Rewriting queries with arbitrary aggregation functions using views

Equivalences among aggregate queries with negation

Aggregation: Expressiveness and Containment

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