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Fast In-Place Verification of Data Dependencies
April 1993 (vol. 5 no. 2)
pp. 266-281

Several fast and space-optimal sequential and parallel algorithms for solving the satisfaction problem of functional and multivalued dependencies (FDs and MVDs) are presented. Two frameworks to verify an MVD for a relation and their implementation by exploring the existing fast space-optimal sorting techniques are described. The space optimality means that only a constant amount of extra memory space is needed for the sequential implementations, and O(M) amount of extra memory space for parallel algorithms that use M processors. This feature makes the algorithms attractive whenever space is a critical resource and I/O transfers should be reduced to the minimal, as is often the case for relational database systems. The time requirements for in-place FD and MVD verification are given in terms of M and of N, which is the number of tuples in a relation. The effect of relation modification on FD and MVD verification is examined.

[1] A. V. Aho, C. Beeri, and J. D. Ullman, "The theory of joins in relational databases,"ACM Trans. Database Syst., vol. 4, no. 3, pp. 314-317, 1979.
[2] W. W. Armstrong, "Dependency structures of data base relationships," inProc. 1974 IFIP Congress, 1974, pp. 580-583.
[3] K. E. Batcher, "Sorting networks and their applications," inProc. AFIPS Spring Joint Computer Conf., 1968, pp. 307-314.
[4] C. Beeri, R. Fagin, and J.H. Howard, "A complete axiomatization for functional and multivalued dependencies," inProc. ACM SIGMOD Conf., 1977, pp. 47-61.
[5] C. Berge,Graphs and Hypergraphs. New York: American Elsevier, 1973.
[6] E. F. Codd, "A relational model of data for large shared data banks,"Commun. ACM, pp. 377-387, June 1970.
[7] R. Fagin, "Multivariate dependencies and a new normal form for relational database,"ACM TODS, vol. 2, no. 3, pp. 262-278, 1977.
[8] R. W. Floyd, "Treesort,"Commun. ACM, vol. 7, p. 701, 1964.
[9] X. Guan and M. A. Langston, "Time-space optimal parallel merging and sorting," inProc. Int. Con. on Parallel Processing, vol. 3, 1989, pp. 1-8.
[10] F. Harary.Graph Theory. Reading, MA: Addison-Wesley, 1969.
[11] B-C Huang and M. A. Langston, "Practical in-place merging,"Commun. ACM, vol. 31, pp. 348-352, 1988.
[12] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[13] D. Maier,The Theory of Relational Databases. Rockville, MD: Computer Science, 1983.
[14] Y. Sagiv, "An algorithm for inferring multivalued dependencies with an application to propositional logic,"J. ACM, vol. 27, pp. 250-262, 1980.
[15] Y. Sagivet al., "An equivalence between relational database dependencies and a fragment of propositional logic,"J. ACM, vol. 28, no. 3, pp. 435-453, July 1981.
[16] J. D. Ullman,Database and Knowledge-base Systems. Rockville, MD: Computer Science Press, 1988.
[17] J. W. J. Williams, "Heapsort,"Commun. ACM, vol. 6, pp. 347-348, 1964.
[18] C. C. Yang,Relational Databases, Englewood Cliffs. NJ, Prentice-Halt, 1986.
[19] C.-C. Yang and W. Shen, "Parallel algorithms for solving the satisfaction problem of functional and multivalued data dependencies,"Data Knowl. Eng., vol. 3, pp. 323-338, 1988.

Index Terms:
in-place verification; data dependencies; space-optimal sequential; parallel algorithms; satisfaction problem; multivalued dependencies; fast space-optimal sorting techniques; space optimality; sequential implementations; I/O transfers; relational database systems; in-place FD; MVD verification; tuples; relation modification; parallel algorithms; program verification; relational databases
L. Li, "Fast In-Place Verification of Data Dependencies," IEEE Transactions on Knowledge and Data Engineering, vol. 5, no. 2, pp. 266-281, April 1993, doi:10.1109/69.219735
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