The higraph, a general kind of diagramming object, forms a visual formalism of topological nature. Higraphs are suited for a wide array of applications to databases, knowledge representation, and, most notably, the behavioral specification of complex concurrent systems using the higraph-based language of statecharts.

On visual formalisms

A class of database schemes, called acychc, was recently introduced. It is shown that this class has a number of desirable properties. In particular, several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity. In addition, several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given, and a smaple algorithm for determining acychclty is presented. Also given are several eqmvalent characterizations of those sets M of multivalued dependencies such that M is the set of muRlvalued dependencies that are the consequences of a given join dependency. Several characterizations for a conflict-free (in the sense of Lien) set of muluvalued dependencies are provided.

On the Desirability of Acyclic Database Schemes

Many real-world situations can be captured by a set of functional dependencies and a single join dependency of a particular form called acyclic [B..]. The join dependency corresponds to a natural decomposition into meaningfull objects (an acyclic database scheme). Our purpose in this paper is to describe efficient algorithms in this setting for various problems, such as computing projections, minimizing joins, inferring dependencies, and testing for dependency satisfaction.

Algorithms for acyclic database schemes

Presented is a computation method—the chase—for testing implication of data dependencies by a set of data dependencies The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman The chase includes previous tableau computation methods as special cases By interpreting tableaux alternately as mappings or as templates for relations, it is possible to test implication of join dependencies (including multivalued dependencies) and functional dependencies by a set of dependencies

Testing implications of data dependencies

Database schemes (winch, intuitively, are collecuons of table skeletons) can be wewed 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.) A class of "acychc" database schemes was recently introduced. A number of basic desirable propemes of database schemes have been shown to be equivalent to acyclicity This shows the naturalness of the concept. However, unlike the situation for ordinary, undirected graphs, there are several natural, noneqmvalent notions of acyclicity for hypergraphs (and hence for database schemes). Various desirable properties of database schemes are constdered and it is shown that they fall into several equivalence classes, each completely characterized by the degree of acycliclty of the scheme The results are also of interest from a purely graph-theoretic viewpomt. The original notion of aeyclicity has the countermtmtive property that a subhypergraph of an acychc hypergraph can be cyclic. This strange behavior does not occur for the new degrees of acyelicity that are considered.

Degrees of acyclicity for hypergraphs and relational database schemes

One problem concerning the universal relation assumption is the inability of known methods to obtain a database scheme design in the general case, where the real-world constraints are given by a set of dependencies that includes embedded multivalued dependencies We propose a simpler method of describing the real world, where constraints are given by functional dependencies and a single join dependency The relationship between this method of defining the real world and the classical methods is exposed We characterize in terms of hypergraphs those multivalued dependencies that are the consequence of a given join dependency Also characterized in terms of hypergraphs are those join dependencies that are equivalent to a set of multivalued dependencies

https://researcher.watson.ibm.com/researcher/files/us-fagin/tods82.pdf

A simplied universal relation assumption and its properties

We investigate the question of when two database schemes embody the same information. We argue that this question reduces to the equivalence of the sets of fixed points of the project-join mappings associated with the two database schemes in question. When data dependencies are given, we need only consider those fixed points that satisfy the dependencies. A polynomial algorithm to test the equivalence of database schemes, when there are no dependencies, is given. We also provide an exponential algorithm to handle the case where there are functional and/or multivalued dependencies. Furthermore, we give a polynomial time test to determine whether a project-join mapping preserves a set of functional dependencies, and a polynomial time algorithm for equivalence of database schemes whose project-join mappings do preserve the given set of functional dependencies. Lastly, we introduce the “update sets” approach to database design as an application of these results.

Equivalence of Relational Database Schemes

Equivalence of relational database schemes

We consider conditions that have appeared in the literature with the purpose of defining a “good” decomposition of a relation scheme. We show that these notions are equivalent in the case that all constraints in the database are functional dependencies. This result solves an open problem of Rissanen. However, for arbitrary constraints the notions are shown to differ.

Alberto O. Mendelzon

Papers

A simplied universal relation assumption and its properties

Equivalence of Relational Database Schemes

Equivalence of relational database schemes

Adequacy of Decompositions of Relational Databases.

Adequacy of Decompositions of Relational Databases