TY - GEN

T1 - Towards tractable algebras for bags

AU - Grumbach, Stephane

AU - Milo, Tova

N1 - Funding Information:
* Work supported in part by the Esprit Project BRA FIDE 2. -E-mail: Stephane.Grumbach inria.fr. E-mail: milo math.tau.ac.il. The research was done while the second author visited INRIA (supported by the Chateaubriand scholarship), and University of Toronto (supported by the Institute for Robotics and Intelligent Systems).

PY - 1993

Y1 - 1993

N2 - Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the relationship between the depth of bag nesting and the expressive power, and (ii) the relationship between the algebraic operations, and their complexity and expressive power. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator.

AB - Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the relationship between the depth of bag nesting and the expressive power, and (ii) the relationship between the algebraic operations, and their complexity and expressive power. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator.

UR - http://www.scopus.com/inward/record.url?scp=0027797979&partnerID=8YFLogxK

U2 - 10.1145/153850.153855

DO - 10.1145/153850.153855

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AN - SCOPUS:0027797979

SN - 0897915933

SN - 9780897915939

T3 - Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

SP - 49

EP - 58

BT - Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

PB - Association for Computing Machinery (ACM)

T2 - Proceedings of the 12th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

Y2 - 25 May 1993 through 28 May 1993

ER -