Abstract
It is well known that the notions of normal forms and acyclicity capture many practical desirable properties for database schemes. The basic schema design problem is to develop design methodologies that strive toward these ideals. The usual approach is to first normalize the database scheme as far as possible. If the resulting scheme is cyclic, then one tries to transform it into an acyclic scheme. In this paper, we argue in favor of carrying out these two phases of design concurrently. In order to do this efficiently, we need to be able to incrementally analyze the acyclicity status of a database scheme as it is being designed. To this end, we propose the formalism of "binary decompositions". Using this, we characterize design sequences that exactly generate θ-acyclic schemes, for θ = α,β. We then show how our results can be put to use in database design. Finally, we also show that our formalism above can be effectively used as a proof tool in dependency theory. We demonstrate its power by showing that it leads to a significant simplification of the proofs of some previous results connecting sets of multivalued dependencies and acyclic join dependencies.
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G. Ausiello, A.D'Atri, and M. Moscarini, "Minimal coverings of acyclic database schemata", Advances in Database Theory, vol.2 (H. Gallaire et al eds.), Plenum Press, 1984.
C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, "On the desirability of acyclic database schemes", JACM 30, 3 (July 1983), 479–513.
C. Beeri and M. Kifer, "Elimination of intersection anomalies from database schemes", Proc. 2nd ACM Symp. PODS, March 1983, pp.340–351.
C. Berge, Graphs and Hypergrapha, North Holland, Amsterdam, 1973.
J. Biskup and H.H. Bruggeman, "Toward designing acyclic database schemas", Proc. ONERA — CERT Workshop on "Logical Bases for Databases", France, Dec. 1982.
K. Chase, "Join graphs and acyclic database schemes", Proc. 7th Int.Conf.VLDB, 1981.
E.F. Codd, "Further normalization of the database relational model", Database Systems (R. Rustin Ed.), Prentice Hall, Englewood Cliffs, NJ, 1972, pp. 33–64.
A. D'Atri and M. Moscarini, "On the recognition and design of acyclic databases", Proc. 3rd ACM Symp. PODS, 1984, pp. 1–8.
R. Fagin, "Degrees of acyclicity for hypergraphs and relational database schemes", JACM 30, 3(July 1983), 514–550.
R. Fagin, "Acyclic database schemes (of various degrees): a painless introduction", CAAP'83 8th Collog. on Trees, Algebras, and Programming, (G. Ausiello and M. Protasi, eds.), Springer Verlag, 1983, pp. 65–89.
R. Fagin, A.O. Mendelzon, and J.D. Ullman, "A simplified universal relation assumption and its properties", ACM TODS 2,3 (Sept. 1982), 343–360.
N. Goodman and O. Schmueli, "Syntactic characterization of tree database schemas", JACM 30,4(Oct. 1983), 767–786.
N. Goodman, O. Schmueli, and Y.C. Tay, "GYO reductions, canonical connections, tree and cyclic schemas and tree projections", Proc. 2nd ACM Symp. PODS, (March 1983), pp. 267–278.
N. Goodman and Y.C. Tay, "Synthesizing fourth normal form relations from multivalued dependencies", Tech. Rep. TR-17-83, Aiken Comp.Lab, Harvard Univ., May 1983.
M.H. Graham, "On the universal relation", Tech. Rep., Univ. of Toronto, Toronto, Sept. 1979.
G. Grahne and K.-J. Raiha, "Dependency characterizations for acyclic database schemes", Proc. 3rd ACM Symp. PODS, 1984, pp.9–18.
M. Gyssens and J. Paredaens, "A decomposition methodology for cyclic databases", Proc. ONERA-CERT Workshop on "Logical Bases for Databases", France, Dec. 1982.
Y. Hanatani, "Elimination of cycles in database schemas", Proc. ONERA-CERT Workshop on "Logical Bases for Databases", France, Dec. 1982.
V.S. Lakshmanan, N. Chandrasekharan, and C.E. Veni Madhavan, "Recognition and top-down generation of β-acyclic database schemes", Proc. 4th Int.Conf.FST & TCS, Bangalore, (Dec.1984), LNCS vol.181, Springer Verlag, 1984.
V.S. Lakshmanan, "Split-freedom and MVD-intersection: a new characterization of multivalued dependencies having conflict-free covers", Proc. EATCS Int.Conf.Database Theory, Rome, Sept. 1986.
V.S. Lakshmanan, "Acyclic hypergraphs, dependency-lattices, and relational database design", Ph.D. Dissertation, Dept. of Computer Science & Automation, Indian Institute of Science, Bangalore, 1986.
V.S. Lakshmanan and C.E. Veni Madhavan, "Syntactic characterizations of β-acyclic database schemes", under preparation.
V.S. Lakshmanan and C.E. Veni Madhavan, "On the structure of α-acyclic database schemes", Tech.Rep. DB3, Dept. of Computer Science & Automation, Indian Inst. of Science, Bangalore, Dec. 1984.
Y.E. Lien, "On the equivalence of database models", JACM 29,2(Apr. 1982), 333–362.
D. Maier, The Theory of Relational Databases, Computer Science Press, Maryland, 1983.
D. Sacca, "On the recognition of coverings of acyclic database hypergraphs", Proc. 2nd ACM Symp. PODS, 1983, pp.297–303.
D. Sacca, "Closure of database hypergraphs", JACM, Oct.1985.
D. Sacca, F. Manfredi, and A. Mecchia, "Properties of database schemata with functional dependencies", Proc. 3rd ACM Symp. PODS, 1984, pp. 19–28.
E. Sciore, "Real-world MVDs", Proc.Int.Conf.Management of Data, ACM, NY, 1981, pp. 121–132.
M. Yannakakis, "Algorithms for acyclic database schemes", Proc. 7th Int.Conf. VLDB, 1981, pp.82–94.
J.D. Ullman, Principles of Database Systems, Computer Science Press, Maryland, 1982.
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Lakshmanan, V.S., Veni Madhavan, C.E. (1986). Binary decompositions and acyclic schemes. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1986. Lecture Notes in Computer Science, vol 241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17179-7_13
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DOI: https://doi.org/10.1007/3-540-17179-7_13
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