Degrees of acyclicity for hypergraphs and relational database schemes

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.

[1]  Ronald Fagin,et al.  Horn clauses and database dependencies , 1982, JACM.

[2]  Ronald Fagin,et al.  A normal form for relational databases that is based on domains and keys , 1981, TODS.

[3]  Nathan Goodman,et al.  Tree queries: a simple class of relational queries , 1982, TODS.

[4]  Carlo Zaniolo,et al.  Analysis and design of relational schemata for database systems. , 1976 .

[5]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[6]  Giorgio Ausiello,et al.  Minimal Coverings of Acyclic Database Schemata , 1982, Advances in Data Base Theory.

[7]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

[8]  Peter Honeyman,et al.  Testing satisfaction of functional dependencies , 1982, JACM.

[9]  Ronald Fagin,et al.  Inclusion Dependencies and Their Interaction with Functional Dependencies , 1984, J. Comput. Syst. Sci..

[10]  Ronald Fagin.  The Decomposition Versus Synthetic Approach to Relational Database Design , 1977, VLDB.

[11]  Charles W. Bachman,et al.  Data structure diagrams , 1969, DATB.

[12]  Catriel Beeri,et al.  Equivalence of relational database schemes , 1979, SIAM J. Comput..

[13]  Alfred V. Aho,et al.  The theory of joins in relational data bases , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[14]  Karen Chase.  Join Graphs and Acyclic Database Schemes , 1981, VLDB.

[15]  Donald D. Chamberlin,et al.  SEQUEL 2: A Unified Approach to Data Definition, Manipulation, and Control , 1976, IBM J. Res. Dev..

[16]  Philip A. Bernstein,et al.  Power of Natural Semijoins , 1981, SIAM J. Comput..

[17]  David Maier,et al.  Connections in acyclic hypergraphs: extended abstract , 1982, PODS '82.

[18]  Yehoshua Sagiv,et al.  Can we use the universal instance assumption without using nulls? , 1981, SIGMOD '81.

[19]  Y. Edmund Lien,et al.  On the Equivalence of Database Models , 1982, JACM.

[20]  Marina Moscarini,et al.  Formal Tools for Top-Down and Bottom-Up Generation of Acyclic Relational Schemata , 1981, WG.

[21]  Jorma Rissanen.  Theory of Relations for Databases - A Tutorial Survey , 1978, MFCS.

[22]  Catriel Beeri,et al.  Properties of acyclic database schemes , 1981, STOC '81.

[23]  Ronald Fagin,et al.  A simplied universal relation assumption and its properties , 1982, TODS.

[24]  Jeffrey D. Ullman,et al.  The U. R. strikes back , 1982, PODS.

[25]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[26]  Mihalis Yannakakis,et al.  Algorithms for Acyclic Database Schemes , 1981, VLDB.

[27]  Clement T. Yu,et al.  An algorithm for tree-query membership of a distributed query , 1979, COMPSAC.

[28]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[29]  Paolo Atzeni,et al.  Assumptions in relational database theory , 1982, PODS '82.

[30]  David Maier,et al.  The revenge of the JD , 1983, PODS '83.