The implication problem for functional and multivalued dependencies : An algebraic approach
 V. S. Lakshmanan,
 C. E. Veni Madhavan
 … show all 2 hide
Abstract
Computation of the dependency basis is the fundamental step in solving the implication problem for MVDs in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of an MVDlattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVDlattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a) computing the inference basis of a given set M of MVDs; (b) computing the dependency basis of a given attribute set w.r.t. M; and (c) solving the implication problem for MVDs. Finally, we show that our results naturally extend to incorporate FDs also in a way that enables the solution of the implication problem for both FDs and MVDs put together.
 W.W. Armstrong, "Dependency structures of database relationships", Proc. IFIP 74, North Holland, Amsterdam, 1974, pp.580–583.
 C. Beeri, "On the membership problem for functional and multivalued dependencies in relational databases", ACM TODS 5,3 (Sept. 1980), 241–249. CrossRef
 C. Beeri, R. Fagin, and J.H. Howard, "A complete axiomatization for functional and multivalued dependencies in database relations", Proc. ACM SIGMOD Int.Conf. on Management of Data, Toronto, Aug.1977, pp.47–61.
 C. Beeri and M.Y. Vardi, "On the properties of join dependencies", in: Advances in Database Theory Vol.I (H. Gallaire, J. Minker, and J. Nicolas, Eds.), Plenum Press, NY, 1981, pp.25–71.
 G. Birkhoff, Lattice Theory, 3rd ed., Providence, RI: American, Mathematical Society Colloquium Publ. XXV, 1967.
 J. Biskup, "Inferences of multivalued dependencies in fixed and undetermined universes", Theor.Comput.Sci. 10, 1(Jan.1980),93–105. CrossRef
 E.F. Codd, "A relational model of data for large shared data banks", CACM 13, 6(June 1970), 377–387.
 —, "Further normalization of the database relational model", in: Data Base Systems (R. Rustin Ed.), Prentice Hall, Englewood Cliffs, NJ, pp.33–64.
 C. Delobel, "Semantics of relations and decomposition process in the relational data model", ACM TODS 3,3 (Sept. 1978), 201–222. CrossRef
 R. Fagin, "Multivalued dependencies and a new normal form for relational databases", ACM TODS 2,3 (Sept.1977), 262–278. CrossRef
 Z. Galil, "An almost lineartime algorithm for computing a dependency basis in a relational database", JACM 29, 1(Jan. 1982), 96–102. CrossRef
 K. Hagihara, et al, "Decision problems for multivalued dependencies in relational databases", SIAM J. Comput. 8,2 (May 1979), 247–264. CrossRef
 W. Kent, "A guide to the five normal forms in relational database theory", CACM 1983.
 V.S. Lakshmann and C.E. Veni Madhavan, "An algebraic theory of functional and multivalued dependencies in relational databases", under preparation.
 T.T. Lee, "An algebraic theory of relational databases", The Bell Syst. Tech. Jl.62, 10 (Dec.1983), 3159–3204.
 —, "Orderpreserving representations of the partitions on the finite set", J.Combinatorial Theory, Series A 31, No.2 (Sept.1981), 136–145. CrossRef
 A.O. Mendelzon, "On axiomatizing multivalued dependencies in relational databases", JACM 26, 1(Jan.1979), 37–44. CrossRef
 K.K. Nambiar, "A study of saturated sets and functional dependencies in relational databases using linear graphs", Proc. 1st Conf. FST and TCS, Bangalore, India, Dec.1981, pp.99–108.
 Y. Sagiv, "An algorithm for inferring multivalued dependencies with an application to propositional logic", JACM 27,2 (April 1980), 250–262. CrossRef
 Y. Sagiv, et al, "An equivalence between relational database dependencies and a subclass of propositional logic", JACM 28,3 (July 1981), 435–453. CrossRef
 J.D. Ullman, Principles of Database Systems, Computer Science Press, Potmac, Maryland 1983.
 M.Y. Vardi, "Inferring multivalued dependencies from functional and join dependencies", Acta Informatica,19(1983), 305–324. CrossRef
 C. Zaniolo, "Analysis and design of relational schemata for database systems", Tech.Rep.UCLA_ENG_7769, Dept. of Comp.Sci., UCLA, July 1976.
 Title
 The implication problem for functional and multivalued dependencies : An algebraic approach
 Book Title
 Foundations of Software Technology and Theoretical Computer Science
 Book Subtitle
 Fifth Conference, New Delhi, India December 16–18, 1985 Proceedings
 Pages
 pp 303328
 Copyright
 1985
 DOI
 10.1007/3540160426_17
 Print ISBN
 9783540160427
 Online ISBN
 9783540397229
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 206
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Authors

 V. S. Lakshmanan ^{(1)}
 C. E. Veni Madhavan ^{(1)}
 Author Affiliations

 1. School of Automation, Indian Institute of Science, 560 012, Bangalore, India
Continue reading...
To view the rest of this content please follow the download PDF link above.