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Algebraic equivalences of nested relational operators

2005
*
Information Systems
*

The join

doi:10.1016/j.is.2003.12.001
fatcat:w6hh3nxtunbvzecmcdedw6yyta
*operation*is one*of*the most time-consuming*operations*in*nested**relational*query processing. ... In this paper, we consider this issue and investigate some*algebraic*properties concerning the*nested**relational**operators*. ...*Equivalences**of**nested**relational**operators*In this section, we investigate some*algebraic*properties concerning the*nested**relational**operators*. ...##
###
The powerset algebra as a natural tool to handle nested database relations

1992
*
Journal of computer and system sciences (Print)
*

In Section 4, we consider the least fixpoint

doi:10.1016/0022-0000(92)90041-g
fatcat:tde37d6ttngipc6uu3yskrkp6a
*operator*and establish the*equivalence**of*the least Iixpoint closure*of*the*nested**algebra*, the powerset*algebra*and the least lixpoint closure*of*the powerset ... In this paper, we investigate other extensions*of*the*nested**relational**algebra*. In order to be able to express transitive closure, one can augment the*nested**algebra*with a least fixpoint*operator*. ... The first author also acknowledges the financial support*of*IBM Belgium, which enabled him to visit Indiana University, where this joint research was performed. ...##
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A comparison between algebraic query languages for flat and nested databases

1991
*
Theoretical Computer Science
*

While the redundancy

doi:10.1016/0304-3975(91)90327-x
fatcat:7lmsnd5o45fqlch5fode7v6oi4
*of*the*nest**operator*might have been expected, the same cannot be said*of*the difference. ... We show that either*nest*or difference can be removed as a primitive*operator*in the powerset*algebra*. ... to be*equivalent*to certain extensions*of*the*nested**algebra*. ...##
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An extended algebra for constraint databases

1998
*
IEEE Transactions on Knowledge and Data Engineering
*

Thus, the di erence existing between such

doi:10.1109/69.729722
fatcat:ilma452c45dslfyht2j7yobg6i
*algebras*is similar to the di erence existing between the*relational**algebra*and the*nested**relational**algebra*, dealing with only one level*of**nesting*. ... Then, we introduce two distinct classes*of*constraint*algebras*, one based on the*relational**algebra*, and one based on the*nested**relational**algebra*, and we present an*algebra**of*the latter type. ... N-based*algebras*: N-based*algebras*are such that the*nested*semantics*of*the result*of*any query they can express is*equivalent*to the result*of*an*equivalent**nested**relational**algebra*query 1], 2], when ...##
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Algebraic equivalences among nested relational expressions

1994
*
Proceedings of the third international conference on Information and knowledge management - CIKM '94
*

Acknowledgment We thank Evan Harris for reading and helpful corrections

doi:10.1145/191246.191287
dblp:conf/cikm/LiuR94
fatcat:pbr5efdrxnckfio43ygbuql3hu
*of*this paper. ... In this paper, we consider this problem and derive a series*of**algebraic**equivalences*. The join*operation*is one*of*the most expensive and critical issues in*nested**relational*query processing. ... Therefore,*algebraic*properties*of**nested**relational**operators*are Permission to co y without fee all or part*of*this material is 1! ...##
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The powerset algebra as a result of adding programming constructs to the nested relational algebra

1988
*
SIGMOD record
*

slight extension

doi:10.1145/971701.50230
fatcat:zrrh3qarvvac5cdqqjyhn52cii
*of*the powerset*algebra*, thus emphasizing both the strength and the naturalness*of*the powerset*algebra*as a tool to manipulate*nested**relations*, and, at the same time, lndlcatmg more ... In this paper, we discuss augmentations*of*the*nested*relatlonal*algebra*with programmmg constructs, such as while-loops and for-loops We show that the*algebras*obtruned in this way are*equivalent*to a ... Acknowledgment The first author IS a senior research assistant*of*the Belgian National Fund*of*Sclentlfic Research He also wishes to acknowledge the financial support*of*IBM Belgium, which enabled him ...##
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The powerset algebra as a result of adding programming constructs to the nested relational algebra

1988
*
Proceedings of the 1988 ACM SIGMOD international conference on Management of data - SIGMOD '88
*

slight extension

doi:10.1145/50202.50230
dblp:conf/sigmod/GyssensG88
fatcat:nybpv4jzj5cuxont6lwrpd6f6m
*of*the powerset*algebra*, thus emphasizing both the strength and the naturalness*of*the powerset*algebra*as a tool to manipulate*nested**relations*, and, at the same time, lndlcatmg more ... In this paper, we discuss augmentations*of*the*nested*relatlonal*algebra*with programmmg constructs, such as while-loops and for-loops We show that the*algebras*obtruned in this way are*equivalent*to a ... Acknowledgment The first author IS a senior research assistant*of*the Belgian National Fund*of*Sclentlfic Research He also wishes to acknowledge the financial support*of*IBM Belgium, which enabled him ...##
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Equivalence of the relational algebra and calculus for nested relations

1992
*
Computers and Mathematics with Applications
*

The

doi:10.1016/0898-1221(92)90050-r
fatcat:zsknyrsfn5eu5jptscozfpnymu
*relational**algebra*is then augmented with progrmomlng constructs and this augmented*algebra*is shown to be*equivalent*in expressive power to the*relational*calculus for*nested**relations*. ... Since the full powerset cannot be derived from the*algebra**operations*, there does not exist a complete*equivalence*between the calculus and the*algebra*. ... It also includes extended definitions*of**algebra**operations*for*nested**relations*. ...##
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Solving equations in the relational algebra
[article]

2003
*
arXiv
*
pre-print

for

arXiv:cs/0106034v2
fatcat:um7wb55mufgbpabxtktqs3y6ou
*nested**relational*databases,*equivalent*to the well-known powerset*algebra*. ... Enumerating all solutions*of*a*relational**algebra*equation is a natural and powerful*operation*which, when added as a query language primitive to the*nested**relational**algebra*, yields a query language ... The equation*algebra*is extremely powerful: it is*equivalent*to the well-known powerset*algebra*for*nested**relations*. ...##
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Book Review: Nest algebras

1989
*
Bulletin of the American Mathematical Society
*

Singer

doi:10.1090/s0273-0979-1989-15847-3
fatcat:a3utuhgugbhjbfhdykwno6kqpm
*of*a*related*class*of**operator**algebras*, and in the last twenty-five years the subject has matured to the extent that they form a moderately well-understood class in the category*of*non-self-adjoint ... STEPHEN POWER UNIVERSITY*OF*LANCASTER sociated*nest**algebra*T(yV) consists*of*all*operators*which leave invariant each subspace N*of*JV .*Nests*JV and J! ...##
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Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions

2001
*
Theoretical Computer Science
*

Speciÿcally, we show that when only unary at

doi:10.1016/s0304-3975(99)00301-1
fatcat:h3tyftq7mrcuxdei4su6kgxroy
*relations*are into play, any powerset*algebra*expression is either*equivalent*to a*nested**algebra*expression, or its evaluation will produce intermediate results ... Paredaens and Van Gucht proved that the at*relational**algebra*has the same expressive power as the*nested**relational**algebra*, as far as queries over at*relations*and with at results are concerned. ... By canonically generalizing the*operators**of*the*relational**algebra*to work on*nested**relations*, and adding the two*operators**of**nesting*and unnesting [9] , one obtains the*nested**relational**algebra*...##
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Optimization of Nested Queries using the NF2 Algebra

2016
*
Proceedings of the 2016 International Conference on Management of Data - SIGMOD '16
*

First, the NF 2

doi:10.1145/2882903.2915241
dblp:conf/sigmod/HolschGS16
fatcat:eixgcwgaabf2rfu52w3t3nod5q
*algebra*can represent all types*of**nested*queries as well as both existing and novel optimization techniques based on its*equivalences*. ... Second, performance benefits can be achieved with little changes to existing transformation-based query optimizers as the NF 2*algebra*is an extension*of*the*relational**algebra*. ... [19] and Cao and Badia [4] also propose the use*of**nested**relational**algebras*, but assume the presence*of*physical*nest*and unnest*operators*. ...##
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Page 5202 of Mathematical Reviews Vol. , Issue 90I
[page]

1990
*
Mathematical Reviews
*

They obtain similar results for co-Tauberian

*operators*and for various*related*families*of*semigroups*of*opera- tors. O D. G. ... It dis- cusses, briefly, much*of*the essential theory*of**nest**algebras*and how this leads to natural interesting problems for CSL*algebras*(reflexive*operator**algebras*with commutative invariant projection ...##
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Theoretical foundation of algebraic optimization utilizing unnormalized relations
[chapter]

1986
*
Lecture Notes in Computer Science
*

With the

doi:10.1007/3-540-17187-8_48
fatcat:dpohpeqy55e3lpmjbruna74xyu
*equivalence*rules introduced here we prove that efficient*algebraic*optimization can be performed using standard (INF) techniques. Particularly, all redundant joins can be properly removed. ... Unnormalized (NF2)*relations*, not conforming to the first normal form condition (lNF)*of*the*relational*model have been proposed recently for a variety*of*new applications. ... Bernd Paul and Gerhard Weikum have contributed by clarifying discussions on the contents and presentation*of*this paper. Liz Klinger needed little TEXnical support to do the typing. ...##
###
Page 1051 of Mathematical Reviews Vol. , Issue 88b
[page]

1988
*
Mathematical Reviews
*

All but one

*of*the*operators*in the*algebra*are analogues*of**operators*in the*algebra*for the*relational*model, but are ex- tended to take advantage*of*the recursive structure*of*Verso rela- tions. ... The paper demonstrates that the Verso*algebra*is at least as powerful as the*relational**algebra*, by showing that any*algebraic**operation*performed on a*relational*database which corresponds to a Verso ...
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