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Cartesian Product

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  • First Online:
Encyclopedia of Database Systems

  • 44 Accesses

Synonyms

Cross product

Definition

Given two relation instances R 1, over set of attributes U 1, and R 2, over set of attributes U 2 – with U 1 and U 2 disjoint – the Cartesian product R 1 Ã— R 2 returns a new relation, over set of attributes U 1 ∪ U 2, consisting of tuples {t|t(U 1) ∈ R 1 and t(U 2) ∈ R 2}. Here t(U) denotes the restriction of the tuple t to attributes in the set U.

Key Points

The Cartesian product is an operator of the relational algebra which extends to relations the usual notion of Cartesian product of sets.

Since the sets of attributes of the input relations are disjoint, in R 1 Ã— R 2, each tuple of R 1 is combined with each tuple of R 2; moreover the arity of the output relation is the sum of the arities of R 1 and R 2.

As an example, consider a relation Students over attributes (student-number, student-name), containing tuples {(1001, Black), (1002, White)}, and a relation Courses over attributes (course-number, course-name), containing tuples {(EH1, Databases), (

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Authors and Affiliations

  1. IRIF, Paris Diderot University, Paris, France

    Cristina Sirangelo

Authors
  1. Cristina Sirangelo
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Correspondence to Cristina Sirangelo .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, Georgia, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, Ontario, Canada

    M. Tamer Özsu

Section Editor information

  1. School of Informatics, University of Edinburgh, Crichton Street, EH8 9LE, Edinburgh, Scotland, UK

    Leonid Libkin

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Sirangelo, C. (2017). Cartesian Product. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_1259-2

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  • DOI: https://doi.org/10.1007/978-1-4899-7993-3_1259-2

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4899-7993-3

  • Online ISBN: 978-1-4899-7993-3

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