Abstract
A databaseR has some obvious and less obvious parameters such as the number of attributes, the size |r|, the maximum size of a domain, the number of some special functional dependencies (e.g. the minimal keys), and so on. The main aim of this paper is to survey some of the results giving connections and inequalities among these parameters. The methods are of a combinatorial nature. A generalization of the numerical dependency is also considered.
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References
V.B. Alekseyev, Diskret. Mat. 1(1989)129–136.
W.W. Armstrong, Dependency structures of data base relationship, in:Information Processing 74 (North-Holland, Amsterdam) pp. 580–583.
A. Békéssy, J. Demetrovics, L. Hannák, P. Frankl and G.O.H. Katona, On the number of maximal dependencies in a data base relation of fixed order, Discr. Math. 30(1980)83–88.
F.E. Bennett and Lisheng Wu, On minimum matrix representation of closure operations, Discr. Appl. Math. 26(1990)25–40.
J. Biskup, private communication.
B. Bollobás, On generalized graphs, Acta Math. Hungar. 16(1965)447–452.
Yeow Meng Chee, Design-theoretic problems in perfectly (n-3)-error-correcting databases, SIAM J. Discr. Math., submitted.
E.F. Codd, A relational model of data for large shared data banks, Commun. ACM 13(1970)377–387.
G. Burosch, J. Demetrovics and G.O.H. Katona, The poset of closures as a model of changing databases, Order 4(1987)127–142.
G. Burosch, J. Demetrovics, G.O.H. Katona, D.J. Kleitman and A.A. Sapozhenko, On the number of database closure operations, Theor. Comput. Sci. 78(1991)377–381.
G. Burosch, J. Demetrovics, G.O.H. Katona, D.J. Kleitman and A.A. Sapozhenko, On the number of database closure operations, II, Discr. Appl. Math., submitted.
J. Demetrovics, On the equivalence of candidate keys with Sperner systems, Acta Cybern. 4(1979)247–252.
J. Demetrovics, Z. Füredi and G.O.H. Katona, Minimum matrix representation of closure operations, Discr. Appl. Math. 11(1985)115–128.
J. Demetrovics and Gy. Gyepesi, A note on minimal matrix representation of closure operations, Combinatorica 3(1983)177–180.
J. Demetrovics, G. Hencsey, L.O. Libkin and I.B. Muchnik, On the interaction between closure operations and choice functions with applications to relational databases, Acta Cybem., to appear.
J. Demetrovics and G.O.H. Katona, Extremal combinatorial problems in a relational database, in:Fundamentals of Computation Theory 81, Proc. 1981 Int. FCT-Conf., Szeged, Hungary, 1981, Lecture Notes in Computer Science 117 (Springer, Berlin, 1981) pp. 110–119.
J. Demetrovics and G.O.H. Katona, Combinatorial problems of database models, in:Coll. Math. Soc. János Bolyai, 42. Algebra, Combinatorics and Logic in Computer Science, Györ, Hungary, 1983 (North-Holland, Amsterdam, 1986) pp. 331–353.
J. Demetrovics and G.O.H. Katona, Extremal combinatorial problems of databases, in:MFDBS'87, 1st Symp. on Mathematical Fundamentals of Database Systems, Dresden, Germany, Lecture Notes in Computer Science (Springer, 1987) pp. 99–127.
J. Demetrovics, G.O.H. Katona and D. Miklós, Partial dependencies in relational databases and their realization, Discr. Appl. Math., to appear.
J. Demetrovics, G.O.H. Katona and A. Sali, On the characterization of branching dependencies, Discr. Appl. Math., to appear.
J. Demetrovics, G.O.H. Katona and A. Sali, Branching dependencies in relational databases (in Hungarian), Alkalmaz. Mat Lapok, to appear.
J. Demetrovics and Son Hua Nam, Closures and Sperner families,Coll. Math. Soc. János Bolyai, Extremal Problems for Families of Subsets, Visegrád, Hungary (1991), submitted.
Z. Füredi, Perfect error-correcting databases, Discr. Appl. Math. 28(1990)171–176.
J. Grant and J. Minker, Normalization and axiomatization for numerical dependencies, Inf. Contol 65(1985)1–17.
H.-O.O.F. Gronau and B. Ganter, On two conjectures of Demetrovics, Füredi and Katona concerning partitions, Discr. Math. 88(1991)149–155.
H.-O.O.F. Gronau and R.C. Mullin, Preprint.
A.D. Korshunov, On the number of monotone Boolean functions, Problemy Kibernet. 38(1981)5–108, in Russian.
A.V. Kostochka, On the maximum size of a filter in then-cube, Metodi Diskretnovo Analiza 41(1984)49–61, in Russian.
D. Lubell, A short proof of Sperner's lemma, J. Combinat Theory 1(1966)299.
H. Mannila and K.-J. Räihä, On the complexity of inferring functional dependencies, Discr. Appl. Math., to appear.
L.D. Meshalkin, A generalization of Sperner's theorem on the number of subsets of a finite set, Teor. Veroyatnost. i Primenen. 8(1963)219–220, in Russian.
A. Rausche, On the existence of special block designs, Rostock Math. Kolloq. 35(1985)13–20.
A. Sali, Extremal problems for finite partially ordered sets and matrices, Thesis for “kandidátus” degree, Hungarian Academy of Sciences, Budapest (1990), in Hungarian.
A. Sali, private communication.
E. Sperner, Ein Satz über Untermengen einer endlichen Menge, Math. Z. 27(1928)544–548.
B. Thalheim, A review of research on dependency theory in relational databases I, II, Preprint, Technische Universität Dresden, Sektion Mathematik (1986).
B. Thalheim, On the number of keys in relational databases, Discr. Appl. Math., to appear.
B. Thalheim,Dependencies in Relational Databases (Teubner, Leipzig, 1991).
K. Yamamoto, Logarithmic order of free distributive lattices, J. Math. Soc. Japan 6(1954)347–357.
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This work was supported by the Hungarian National Foundation for Scientific Research, Grant No. 2575.
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Demetrovics, J., Katona, G.O.H. A survey of some combinatorial results concerning functional dependencies in database relations. Ann Math Artif Intell 7, 63–82 (1993). https://doi.org/10.1007/BF01556350
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DOI: https://doi.org/10.1007/BF01556350
