On the Existence of Armstrong Data Trees for XML Functional Dependencies

  • Sven Hartmann
  • Henning Köhler
  • Thu Trinh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5956)


Armstrong databases are a popular tool in example-based database design. An Armstrong database for a given constraint set Σ from a fixed constraint class \(\mathcal Z\) satisfies precisely those constraints from \(\mathcal Z\) that are logically implied by Σ. In this paper we study Armstrong data trees for functional dependencies for XML-encoded data in the context of a simple XML tree model reflecting the permitted parent-child relationships together with their frequencies.


Relational Database Functional Dependency Data Tree Integrity Constraint Constraint Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arenas, M., Fan, W., Libkin, L.: What’s hard about XML schema constraints? In: Hameurlain, A., Cicchetti, R., Traunmüller, R. (eds.) DEXA 2002. LNCS, vol. 2453, pp. 269–278. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Arenas, M., Libkin, L.: A normal form for XML documents. ACM ToDS 29, 195–232 (2004)CrossRefGoogle Scholar
  3. 3.
    Armstrong, W.W.: Dependency structures of data base relationships. In: IFIP, pp. 580–583 (1974)Google Scholar
  4. 4.
    Atzeni, P., Morfuni, N.M.: Functional dependencies and constraints on null values in database relations. Inform. and Control 70, 1–31 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Baixeries, J., Balcázar, J.L.: Characterization and Armstrong relations for degenerate multivalued dependencies using formal concept analysis. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 162–175. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Beeri, C., Dowd, M., Fagin, R., Statman, R.: On the structure of Armstrong relations for functional dependencies. J. ACM 31, 30–46 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Beeri, C., Fagin, R., Howard, J.H.: A complete axiomatization for functional and multivalued dependencies in database relations. In: SIGMOD, pp. 47–61. ACM, New York (1977)Google Scholar
  8. 8.
    De Marchi, F., Lopes, S., Petit, J.-M.: Informative Armstrong relations: Application to database analysis. In: BDA (2001)Google Scholar
  9. 9.
    De Marchi, F., Lopes, S., Petit, J.-M., Toumani, F.: Analysis of existing databases at the logical level: the DBA companion project. SIGMOD Rec. 32, 47–52 (2003)CrossRefGoogle Scholar
  10. 10.
    De Marchi, F., Petit, J.-M.: Semantic sampling of existing databases through informative Armstrong databases. Inf. Syst. 32, 446–457 (2007)CrossRefGoogle Scholar
  11. 11.
    Demetrovics, J., Gyepesi, G.: A note on minimal matrix representation of closure operations. Combinatorica 3, 177–179 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Demetrovics, J., Katona, G.O.H.: A survey of some combinatorial results concerning functional dependencies. Ann. Math. Artificial Intelligence 7, 63–82 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Demetrovics, J., Katona, G.O.H., Sali, A.: The characterization of branching dependencies. Discrete Appl. Math. 40, 139–153 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Demetrovics, J., Katona, G.O.H., Sali, A.: Design type problems motivated by database theory. J. Statist. Plann. Inference 72, 149–164 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Demetrovics, J., Libkin, L., Muchnik, I.B.: Functional dependencies in relational databases: A lattice point of view. Discrete Appl. Math. 40, 155–185 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Demetrovics, J., Rónyai, L., Nam Son, H.: On the representation of dependencies by propositional logic. In: Thalheim, B., Gerhardt, H.-D., Demetrovics, J. (eds.) MFDBS 1991. LNCS, vol. 495, pp. 230–242. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  17. 17.
    Demetrovics, J., Thi, V.D.: Armstrong relations, functional dependencies and strong dependencies. Comp. Artif. Intell. 14 (1995)Google Scholar
  18. 18.
    Demetrovics, J., Thi, V.D.: Some observations on the minimal Armstrong relations for normalised relation schemes. Comp. Artif. Intell. 14 (1995)Google Scholar
  19. 19.
    Demetrovics, J., Thi, V.D.: Some remarks on generating Armstrong and inferring functional dependencies relation. Acta Cybernet. 12, 167–180 (1995)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Fagin, R.: Horn clauses and database dependencies. J. ACM 29, 952–985 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Fagin, R., Vardi, M.Y.: Armstrong databases for functional and inclusion dependencies. Inf. Process. Lett. 16, 13–19 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Fan, W.: XML constraints. In: DEXA Workshops, pp. 805–809. IEEE, Los Alamitos (2005)Google Scholar
  23. 23.
    Fan, W., Libkin, L.: On XML integrity constraints in the presence of DTDs. J. ACM 49(3), 368–406 (2002)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Fan, W., Siméon, J.: Integrity constraints for XML. J. Comput. Syst. Sci. 66(1), 254–291 (2003)CrossRefzbMATHGoogle Scholar
  25. 25.
    Felea, V.: Armstrong-like relations for functional partition dependencies. Sci. Ann. Cuza Univ. 1, 69–76 (1992)zbMATHMathSciNetGoogle Scholar
  26. 26.
    Gottlob, G., Libkin, L.: Investigation on Armstrong relations, dependency inference, and excluded functional dependencies. Acta Cybernet. 9, 385–402 (1990)zbMATHMathSciNetGoogle Scholar
  27. 27.
    Gunopulos, D., Khardon, R., Mannila, H., Saluja, S., Toivonen, H., Sharma, R.S.: Discovering all most specific sentences. ACM ToDS 28, 140–174 (2003)CrossRefGoogle Scholar
  28. 28.
    Hartmann, S.: On the implication problem for cardinality constraints and functional dependencies. Ann. Math. Artificial Intelligence 33, 253–307 (2001)CrossRefGoogle Scholar
  29. 29.
    Hartmann, S., Leck, U., Link, S.: On matrix representations of participation constraints. In: Heuser, C.A., Pernul, G. (eds.) ER 2009 Workshops. LNCS, vol. 5833, pp. 75–84. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  30. 30.
    Hartmann, S., Link, S.: More functional dependencies for XML. In: Kalinichenko, L.A., Manthey, R., Thalheim, B., Wloka, U. (eds.) ADBIS 2003. LNCS, vol. 2798, pp. 355–369. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  31. 31.
    Hartmann, S., Link, S., Kirchberg, M.: A subgraph-based approach towards functional dependencies for XML. In: SCI, IIIS, pp. 200–205 (2003)Google Scholar
  32. 32.
    Hartmann, S., Trinh, T.: Axiomatising functional dependencies for XML with frequencies. In: Dix, J., Hegner, S.J. (eds.) FoIKS 2006. LNCS, vol. 3861, pp. 159–178. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  33. 33.
    Jungnickel, D.: Graphs, Networks and Algorithms. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  34. 34.
    Katona, G.O.H.: Combinatorial and algebraic results for database relations. In: Hull, R., Biskup, J. (eds.) ICDT 1992. LNCS, vol. 646, pp. 1–20. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  35. 35.
    Katona, G.O.H., Sali, A.: New type of coding problem motivated by database theory. Discrete Appl. Math. 144, 140–148 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Katona, G.O.H., Tichler, K.: Some contributions to the minimum representation problem of key systems. In: Dix, J., Hegner, S.J. (eds.) FoIKS 2006. LNCS, vol. 3861, pp. 240–257. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  37. 37.
    Lee, M.-L., Ling, T.W., Low, W.L.: Designing functional dependencies for XML. In: Jensen, C.S., Jeffery, K., Pokorný, J., Šaltenis, S., Bertino, E., Böhm, K., Jarke, M. (eds.) EDBT 2002. LNCS, vol. 2287, pp. 124–141. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  38. 38.
    Levene, M., Loizou, G.: Axiomatisation of functional dependencies in incomplete relations. Theoret. Comput. Sci. 206, 283–300 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  39. 39.
    Levene, M., Loizou, G.: Database design for incomplete relations. ACM ToDS 24, 80–125 (1999)CrossRefGoogle Scholar
  40. 40.
    Lien, Y.E.: On the equivalence of database models. J. ACM 29, 333–362 (1982)CrossRefzbMATHGoogle Scholar
  41. 41.
    Liu, J., Vincent, M., Liu, C.: Functional dependencies, from relational to XML. In: PSI, pp. 531–538 (2003)Google Scholar
  42. 42.
    Lopes, S., Petit, J.-M., Lakhal, L.: Efficient discovery of functional dependencies and Armstrong relations. In: Zaniolo, C., Grust, T., Scholl, M.H., Lockemann, P.C. (eds.) EDBT 2000. LNCS, vol. 1777, pp. 350–364. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  43. 43.
    Mannila, H., Räihä, K.-J.: Small Armstrong relations for database design. In: PODS, pp. 245–250. ACM, New York (1985)Google Scholar
  44. 44.
    Mannila, H., Räihä, K.-J.: Design by example: An application of Armstrong relations. J. Comput. Syst. Sci. 33, 126–141 (1986)CrossRefzbMATHGoogle Scholar
  45. 45.
    Mannila, H., Räihä, K.-J.: Design of Relational Databases. Addison-Wesley, Reading (1992)zbMATHGoogle Scholar
  46. 46.
    Sali, A.: Minimal keys in higher-order datamodels. In: Seipel, D., Turull-Torres, J.M.a. (eds.) FoIKS 2004. LNCS, vol. 2942, pp. 242–251. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  47. 47.
    Sali, A., Schewe, K.-D.: Keys and Armstrong databases in trees with restructuring. Acta Cybernet. 18, 529–556 (2008)zbMATHMathSciNetGoogle Scholar
  48. 48.
    Sali, A., Székely, L.A.: On the existence of Armstrong instances with bounded domains. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 151–157. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  49. 49.
    Silva, A.M., Melkanoff, M.A.: A method for helping discover the dependencies of a relation. In: Advances in Data Base Theory, pp. 115–133 (1979)Google Scholar
  50. 50.
    Suciu, D.: On database theory and XML. SIGMOD Rec. 30, 39–45 (2001)CrossRefGoogle Scholar
  51. 51.
    Thalheim, B.: Entity-Relationship Modeling. Springer, Heidelberg (2000)CrossRefzbMATHGoogle Scholar
  52. 52.
    Thi, V.D., Son, N.H.: On Armstrong relations for strong dependencies. Acta Cybernet. 17 (2006)Google Scholar
  53. 53.
    Tichler, K.: Minimum matrix representation of some key system. Discrete Appl. Math. 117, 267–277 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  54. 54.
    Tichler, K.: Extremal theorems for databases. Ann. Math. Artificial Intelligence 40, 165–182 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  55. 55.
    Trinh, T.: Functional dependencies for XML: Axiomatisation and normal form in the presence of frequencies and identifiers. MSc thesis, Massey University (2004)Google Scholar
  56. 56.
    Vianu, V.: A web odyssey: from Codd to XML. SIGMOD Rec. 32, 68–77 (2003)CrossRefGoogle Scholar
  57. 57.
    Vincent, M.W., Liu, J.: Functional dependencies for XML. In: Zhou, X., Zhang, Y., Orlowska, M.E. (eds.) APWeb 2003. LNCS, vol. 2642, pp. 22–34. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  58. 58.
    Vincent, M., Liu, J.: Strong functional dependencies and a redundancy free normal form for XML. In: SCI, IIIS, pp. 218–223 (2003)Google Scholar
  59. 59.
    Vincent, M., Liu, J., Liu, C.: Redundancy free mappings from relations to XML. In: WAIM, pp. 55–67 (2003)Google Scholar
  60. 60.
    Vincent, M., Liu, J., Liu, C.: Strong functional dependencies and their application to normal forms in XML. ACM ToDS 29, 445–462 (2004)CrossRefGoogle Scholar
  61. 61.
    Vincent, M.W., Srinivasan, B.: Armstrong relations for functional and multivalued dependencies in relational databases. In: ADC, pp. 317–328 (1993)Google Scholar
  62. 62.
    Wang, J., Topor, R.W.: Removing XML data redundancies using functional and equality-generating dependencies. In: ADC, pp. 65–74 (2005)Google Scholar
  63. 63.
    Weddell, G.E.: Reasoning about functional dependencies generalized for semantic data models. ACM ToDS 17, 32–64 (1992)CrossRefMathSciNetGoogle Scholar
  64. 64.
    Yu, C., Jagadish, H.V.: XML schema refinement through redundancy detection and normalization. VLDB J. 17, 203–223 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sven Hartmann
    • 1
  • Henning Köhler
    • 2
  • Thu Trinh
    • 1
  1. 1.Clausthal University of TechnologyGermany
  2. 2.The University of QueenslandBrisbaneAustralia

Personalised recommendations