David Maier
ABSTRACT
We demonstrate a sense in which the equivalence between blocks (subgraphs without articulation points) and biconnected components (subgraphs in which there are two edge-disjoint paths between any pair of nodes) that holds in ordinary graph theory can be generalized to hypergraphs. The result has an interpretation for relational databases that the universal relations described by acyclic join dependencies are exactly those for which the connections among attributes are defined uniquely. We also exhibit a relationship between the process of Graham reduction [6] of hypergraphs and the process of tableau reduction [1] that holds only for acyclic hypergraphs.
- Aho, A. V., Y. Sagiv, and J. D. Ullman, "Equivalence of relational expressions," SIAM J. Computing 8:2 (1979), pp. 218-246.Google Scholar
Digital Library
- Berge, C., Graphs and Hypergraphs, North Holland, Amsterdam, 1973. Google ScholarDigital Library
- Beeri, C., R. Fagin, D. Maier, and M. Yannakakis, "On the desirable properties of acyclic database schemas," RJ3131, IBM, San Jose, Calif.Google Scholar
- Bernstein, P. A. and N. Goodman, "The theory of semi-joins," TR CCA-79-27, Computer Corp. of America, Cambridge, Mass., 1979.Google Scholar
- Fagin, R., A. O. Mendelzon, and J. D. Ullman, "A simplified universal relation assumption and its properties," RJ2900, IBM, San Jose, Calif., Nov., 1980.Google Scholar
- Graham, M. H., "On the universal relation," technical report, Univ. of Toronto, Sept., 1979.Google Scholar
- Maier, D. and J. D. Ullman, "Maximal objects and the semantics of universal relation databases," TR-80-016, Dept. of C. S., SUNY, Stony Brook, N. Y., 1980.Google Scholar
- Yu, C. T. and M. Z. Ozsoyoglu, "An algorithm for tree-query membership of a distributed query," COMPSAC-79, pp. 306-312, 1979.Google Scholar
- Zaniolo, C., "Analysis and design of relational schemata for database systems," Ph. D. thesis, UCLA, 1976. Google ScholarDigital Library
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