Abstract
In the present paper a distance concept of databases is investigated. Two database instances are of distance 0, if they have the same number of attributes and satisfy exactly the same set of functional dependencies. This naturally leads to the poset of closures as a model of changing database. The distance of two databases (closures) is defined to be the distance of the two closures in the Hasse diagram of that poset. We determine the diameter of the poset and show that the distance of two closures is equal to the natural lower bound, that is to the size of the symmetric difference of the collections of closed sets. We also investigate the diameter of the set of databases with a given system of keys. Sharp upper bounds are given in the case when the minimal keys are 2 (or r)-element sets.
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Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E.: The protein data bank. Nucleic Acids Res. 28(1), 235–242 (2000)
Bhat, T.N., et al.: The PDB data uniformity project. Nucleic Acids Res. 29(1), 214–218 (2001)
Boutselakis, H., et al.: E-MSD: the European Bioinformatics Institute macromolecular structure database. Nucleic Acids Res. 31(1), 458–462 (2003)
Burosch, G., Demetrovics, J., Katona, G.O.H.: The poset of closures as a model of changing databases. Order 4, 127–142 (1987)
De Marchi, F., Petit, J.-M.: Semantic sampling of existing databases through informative Armstrong databases. Inf. Syst. 32, 446–457 (2007)
Demetrovics, J., Katona, G.O.H.: Extremal combinatorial problems in relational data base. In: Lecture Notes in Computer Science, vol. 117, pp. 110–119. Springer, Berlin (1981)
Engel, K.: Sperner Theory. Cambridge University Press, Cambridge (1977)
Erdős, P.: On the number of complete subgraphs contained in certain graphs. Publ. Math. Inst. Hung. Acad. Sci., Ser. A3 VII, 459–464 (1962). http://www.math-inst.hu/~p_erdos/1962-14.pdf
Katona, G.: A theorem on finite sets. In: Theory of Graphs. Proc. Coll. held at Tihany, 1966, Akadémiai Kiadó, pp. 187–207 (1968)
Kolahi, S., Libkin, L.: An information-theoretic analysis of worst-case redundancy in database design. ACM Trans. Database Syst. 35(1) (2010). doi:10.1145/1670243.1670248
Kruskal, J.B.: The number of simplices in a complex. In: Mathematical Optimization Techniques, pp. 251–278. University of California Press, Berkeley and Los Angeles (1963)
Müller, H., Freytag, J.-C., Leser, U.: On the distance of databases. Technical Report, HUB-IB-199 (2006)
Müller, H., Freytag, J.-C., Leser, U.: Describing differences between databases. In: CIKM ’06: Proceedings of the 15th ACM International Conference on Information and Knowledge Management, pp. 612–621. Arlington, VA, USA (2006)
Rother, K., Müller, H., Trissl, S., Koch, I., Steinke, T., Preissner, R., Frömmel, C., Leser, U.: COLUMBA: multidimensional data integration of protein annotations. In: Int. Workshop on Data Integration in Life Sciences (DILS 2004), Leipzig, Germany (2004)
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Research was partially supported by Hungarian National Research Fund (OTKA) grant no. NK 78439.
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Katona, G.O.H., Sali, A. On the distance of databases. Ann Math Artif Intell 65, 199–216 (2012). https://doi.org/10.1007/s10472-012-9306-x
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DOI: https://doi.org/10.1007/s10472-012-9306-x