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)
Y2 - 25 May 1993 through 28 May 1993
ER -