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 DescriptorsF.4.1 [Mathematical Logic and Formal Languages]: Mathematical LogicG.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 termsAlgorithmsDesignLanguagesManagementTheoryAdditional Key Words and Phrasesacyclichypergraphdatabase schemerelational database