Recognition and top-down generation of β-acyclic database schemes

  • V. S. Lakshmanan
  • N. Chandrasskaran
  • C. E. Veni Madhavan
Session 6 Data Bases
Part of the Lecture Notes in Computer Science book series (LNCS, volume 181)


Database schemes can be viewed as hypergraphs with individual relation schemes corresponding to the edges of a hypergraph. Under this setting, a new class of "acyclic" database schemes was recently introduced and was shown to have a claim to a number of desirable properties. However, unlike the case of ordinary undirected graphs, there are several unequivalent notions of acyclicity of hypergraphs. Of special interest among these are α-, β-, and γ-, degrees of acyclicity, each characterizing an equivalence class of desirable properties for database schemes, represented as hypergraphs. In this paper, two complementary approaches to designing β-acyclic database schemes have been presented. For the first part, a new notion called "independent cycle" is introduced. Based on this, a criterion for β-acyclicity is developed and is shown equivalent to the existing definitions of β-acyclicity. From this and the concept of the dual of a hypergraph, an efficient algorithm for testing β-acyclicity is developed. As for the second part, a procedure is evolved for top-down generation of β-acyclic schemes and its correctness is established. Finally, extensions and applications of ideas are described.


Database Scheme Universal Relation Distinct Edge Hereditary Property Independent Cycle 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • V. S. Lakshmanan
    • 1
  • N. Chandrasskaran
    • 1
  • C. E. Veni Madhavan
    • 1
  1. 1.School of AutomationIndian Institute of ScienceBangaloreIndia

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