Graph-theoretical methods to construct entity-relationship databases
Within the recent years, the entity-relationship approach has become one of the most popular methods in high-level database design. In this approach data are modelled as entity and relationship types. Usually relationship types come along with certain restrictions that influence the structure of databases. Cardinality constraints are the most commonly used class of constraints used to model such restrictions. Database instances satisfying given cardinality constraints are said to be valid. The aim of this paper is to show how to use methods from graph theory to determine the class cardinalities of entity and relationship types in valid databases. We develop algorithms for this purpose and a number of variations of the problem, namely to construct databases of minimum size and linear ternary databases.
KeywordsEntity Type Length Function Relationship Type Database Scheme Cardinality Constraint
Unable to display preview. Download preview PDF.
- M. Aigner, Combinatorial Theory (Springer, Berlin, 1979).Google Scholar
- C. Batini, S. Ceri and S. Navathe, Conceptual database design, An entityrelationship approach (Benjamin Cummings, Redwood, 1992).Google Scholar
- R.E. Bellman. On a routing problem. Quart. Appl. Math. 16 (1958), 87–90.Google Scholar
- P. Chen, The Entity-Relationship Model: Towards a unified view of data. ACM TODS 1,1 (1984), 9–36.Google Scholar
- K. Engel and S. Hartmann, Constructing realizers of semantic entity-relationship schemes (1994), submitted to Discr.Appl.Math.Google Scholar
- D. Jungnickel, Graphen, Netzwerke und Algorithmen (BI-Wissenschaftsverlag, Mannheim, 1990).Google Scholar
- S. Hartmann, Schemes and Satisfiablity, Preprint (1995).Google Scholar
- M. Lenzerini and P. Nobili, On the satisfiability of dependency constraints in Entity-Relationship schemata, Information Systems Vol.15, 4 (1990) 453–461.Google Scholar
- R. Sedgewick, Algorithms (Addison-Wesley, Reading, Mass., 1988).Google Scholar
- B. Thalheim, Foundations of Entity-Relationship Modeling, Annals of Mathematics and Artificial Intelligence 6 (1992).Google Scholar
- B. Thalheim, Fundamentals of Entity-Relationship Models (Springer, Berlin, 1993).Google Scholar
- B. Thalheim, A survey on Database Constraints, Reihe Informatik I-8, UniversitÄt Cottbus (1994).Google Scholar