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Repetitions and permutations of columns in the semijoin algebra

Published online by Cambridge University Press:  05 June 2008

Dirk Leinders  and
Jan Van Den Bussche
Dirk Leinders
Affiliation:
Hasselt University and Transnational University of Limburg Agoralaan, gebouw D, 3590 Diepenbeek Belgium; dirk.leinders@uhasselt.be
Jan Van Den Bussche
Affiliation:
Hasselt University and Transnational University of Limburg Agoralaan, gebouw D, 3590 Diepenbeek Belgium; dirk.leinders@uhasselt.be
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Abstract

Codd defined the relational algebra [E.F. Codd, Communications of the ACM13 (1970) 377–387; E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed., Prentice-Hall (1972) 65–98] as the algebra with operations projection, join, restriction, union and difference. His projection operator can drop, permute and repeat columns of a relation. This permuting and repeating of columns does not really add expressive power to the relational algebra. Indeed, using the join operation, one can rewrite any relational algebra expression into an equivalent expression where no projection operator permutes or repeats columns. The fragment of the relational algebra known as the semijoin algebra, however, lacks a full join operation. Nevertheless, we show that any semijoin algebra expression can still be simulated in a natural way by a set of expressions where no projection operator permutes or repeats columns.

Keywords

Databaserelational algebrasemijoin algebraprojection.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 2 , April 2009 , pp. 179 - 187
Copyright
© EDP Sciences, 2008

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