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On the distance of databases

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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.

Keywords

Distance of databases Keys Antikeys Closures Poset Hasse diagram 

Mathematics Subject Classifications (2010)

68P15 05D05 06A07 

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References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Bhat, T.N., et al.: The PDB data uniformity project. Nucleic Acids Res. 29(1), 214–218 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Boutselakis, H., et al.: E-MSD: the European Bioinformatics Institute macromolecular structure database. Nucleic Acids Res. 31(1), 458–462 (2003)CrossRefGoogle Scholar
  4. 4.
    Burosch, G., Demetrovics, J., Katona, G.O.H.: The poset of closures as a model of changing databases. Order 4, 127–142 (1987)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    De Marchi, F., Petit, J.-M.: Semantic sampling of existing databases through informative Armstrong databases. Inf. Syst. 32, 446–457 (2007)CrossRefGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Engel, K.: Sperner Theory. Cambridge University Press, Cambridge (1977)Google Scholar
  8. 8.
    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 Google Scholar
  9. 9.
    Katona, G.: A theorem on finite sets. In: Theory of Graphs. Proc. Coll. held at Tihany, 1966, Akadémiai Kiadó, pp. 187–207 (1968)Google Scholar
  10. 10.
    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
  11. 11.
    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)Google Scholar
  12. 12.
    Müller, H., Freytag, J.-C., Leser, U.: On the distance of databases. Technical Report, HUB-IB-199 (2006)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Computer ScienceBudapest University of Technology and EconomicsBudapestHungary

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