# Acyclic database schemes (of various degrees): A painless introduction

## Abstract

Database schemes (which, intuitively, are collections of table skeletons) can be viewed as hypergraphs. (A *hypergraph* is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) Unlike the situation for ordinary undirected graphs, there are several natural, nonequivalent notions of acyclicity for hypergraphs (and hence for database schemes). A large number of desirable properties of database schemes fall into a small number of equivalence classes, each completely characterized by the degree of acyclicity of the scheme. This paper is intended to be an informal introduction, in which the focus is mainly on the originally studied (and least restrictive) degree of acyclicity.

## Categories and Subject Descriptors

F.4.1 [**Mathematical Logic and Formal Languages**]: Mathematical Logic G.2.2 [

**Discrete Mathematics**]: Graph Theory —

*Graph algorithms*and

*Trees*H.2.1 [

**Database Management**]: Logical Design —

*Normal forms*and

*Schema and subschema*H.3.3. [Information Storage and Retrieval]: Information Search and Retrieval —

*Query formulation*

## General terms

Algorithms Design Languages Management Theory## Additional Key Words and Phrases

acyclic hypergraph database scheme relational database## Preview

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