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Algebraic equivalences of nested relational operators

Hong-Cheu Liu, Jeffrey X. Yu
2005 Information Systems  
The join 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.  ... 
doi:10.1016/j.is.2003.12.001 fatcat:w6hh3nxtunbvzecmcdedw6yyta

The powerset algebra as a natural tool to handle nested database relations

Marl Gyssens, Dirk Van Gucht
1992 Journal of computer and system sciences (Print)  
In Section 4, we consider the least fixpoint 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.  ... 
doi:10.1016/0022-0000(92)90041-g fatcat:tde37d6ttngipc6uu3yskrkp6a

A comparison between algebraic query languages for flat and nested databases

Marc Gyssens, Dirk Van Gucht
1991 Theoretical Computer Science  
While the redundancy 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.  ... 
doi:10.1016/0304-3975(91)90327-x fatcat:7lmsnd5o45fqlch5fode7v6oi4

An extended algebra for constraint databases

A. Belussi, E. Bertino, B. Catania
1998 IEEE Transactions on Knowledge and Data Engineering  
Thus, the di erence existing between such 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  ... 
doi:10.1109/69.729722 fatcat:ilma452c45dslfyht2j7yobg6i

Algebraic equivalences among nested relational expressions

Hong-Chen Liu, K. Ramamohanarao
1994 Proceedings of the third international conference on Information and knowledge management - CIKM '94  
Acknowledgment We thank Evan Harris for reading and helpful corrections 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!  ... 
doi:10.1145/191246.191287 dblp:conf/cikm/LiuR94 fatcat:pbr5efdrxnckfio43ygbuql3hu

The powerset algebra as a result of adding programming constructs to the nested relational algebra

Marc Gyssens, Dirk van Gucht
1988 SIGMOD record  
slight extension 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  ... 
doi:10.1145/971701.50230 fatcat:zrrh3qarvvac5cdqqjyhn52cii

The powerset algebra as a result of adding programming constructs to the nested relational algebra

Marc Gyssens, Dirk van Gucht
1988 Proceedings of the 1988 ACM SIGMOD international conference on Management of data - SIGMOD '88  
slight extension 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  ... 
doi:10.1145/50202.50230 dblp:conf/sigmod/GyssensG88 fatcat:nybpv4jzj5cuxont6lwrpd6f6m

Equivalence of the relational algebra and calculus for nested relations

Lucy Garnett, Abdullah U. Tansel
1992 Computers and Mathematics with Applications  
The 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.  ... 
doi:10.1016/0898-1221(92)90050-r fatcat:zsknyrsfn5eu5jptscozfpnymu

Solving equations in the relational algebra [article]

Joachim Biskup, Jan Paredaens, Thomas Schwentick, Jan Van den Bussche
2003 arXiv   pre-print
for 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.  ... 
arXiv:cs/0106034v2 fatcat:um7wb55mufgbpabxtktqs3y6ou

Book Review: Nest algebras

Stephen Power
1989 Bulletin of the American Mathematical Society  
Singer 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!  ... 
doi:10.1090/s0273-0979-1989-15847-3 fatcat:a3utuhgugbhjbfhdykwno6kqpm

Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions

Jan Van den Bussche
2001 Theoretical Computer Science  
Speciÿcally, we show that when only unary at 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  ... 
doi:10.1016/s0304-3975(99)00301-1 fatcat:h3tyftq7mrcuxdei4su6kgxroy

Optimization of Nested Queries using the NF2 Algebra

Jürgen Hölsch, Michael Grossniklaus, Marc H. Scholl
2016 Proceedings of the 2016 International Conference on Management of Data - SIGMOD '16  
First, the NF 2 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.  ... 
doi:10.1145/2882903.2915241 dblp:conf/sigmod/HolschGS16 fatcat:eixgcwgaabf2rfu52w3t3nod5q

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  ... 

Theoretical foundation of algebraic optimization utilizing unnormalized relations [chapter]

Marc H. Scholl
1986 Lecture Notes in Computer Science  
With the 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.  ... 
doi:10.1007/3-540-17187-8_48 fatcat:dpohpeqy55e3lpmjbruna74xyu

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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