## Towards Tractable Algebras for Bags (1993)

Citations: | 61 - 4 self |

### BibTeX

@MISC{Grumbach93towardstractable,

author = {Stéphane Grumbach and Tova Milo},

title = {Towards Tractable Algebras for Bags},

year = {1993}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 impact of the depth of bag nesting on the expressive power, and (ii) the complexity and the expressive power induced by the algebraic operations. 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. Invited to a special issue of the Journal of Computer and System Sciences selected from ACM Princ. of Database Systems,...