Abstract
Order dependencies (ODs) describe a relationship of order between lists of attributes in a relational table. ODs can help to understand the semantics of datasets and the applications producing them. They have applications in the field of query optimization by suggesting query rewrites. Also, the existence of an OD in a table can provide hints on which integrity constraints are valid for the domain of the data at hand. This work is the first to describe the discovery problem for order dependencies in a principled manner by characterizing the search space, developing and proving pruning rules, and presenting the algorithm Order, which finds all order dependencies in a given table. Order traverses the lattice of permutations of attributes in a level-wise bottom-up manner. In a comprehensive evaluation, we show that it is efficient even for various large datasets.
Similar content being viewed by others
References
Abedjan, Z., Golab, L., Naumann, F.: Profiling relational data: a survey. VLDB J. 24(4), 557–581 (2015)
Abedjan, Ziawasch, Naumann, Felix: Advancing the discovery of unique column combinations. In: Proceedings of the International Conference on Information and Knowledge Management (CIKM), pp. 1565–1570, (2011)
Agrawal, R., Srikant, R.: Fast algorithms for mining association rules in large databases. In: Proceedings of the International Conference on Very Large Databases (VLDB), pp. 487–499, (1994)
De Marchi, F., Lopes, S., Petit, J.-M.: Unary and n-ary inclusion dependency discovery in relational databases. J. Intell. Inf. Syst. 32(1), 53–73 (2009)
Dong, J., Hull, R.: Applying approximate order dependency to reduce indexing space. In: Proceedings of the International Conference on Management of Data (SIGMOD), pp. 119–127, (1982)
Ginsburg, S., Hull, R.: Order dependency in the relational model. Theoret. Comput. Sci. 26(1–2), 149–195 (1983)
Golab, L., Karloff, H.J., Korn, F., Saha, A., Srivastava, D.: Sequential dependencies. Proc. VLDB Endow. 2(1), 574–585 (2009)
Halbeisen, L., Hungerbühler, N.: Number theoretic aspects of a combinatorial function. Notes Numb. Theory Discrete Math. 5(4), 138–150 (1999)
Heise, A., Quiané-Ruiz, J.-A., Abedjan, Z., Jentzsch, A., Naumann, F.: Scalable discovery of unique column combinations. Proc. VLDB Endow. 7(4), 301–312 (2013)
Huhtala, Y., Kärkkäinen, J., Porkka, P., Toivonen, H.: TANE: an efficient algorithm for discovering functional and approximate dependencies. Comput. J. 42(2), 100–111 (1999)
Lichman, M.: UCI machine learning repository. University of California, Irvine, School of Information and Computer Sciences (2013). http://archive.ics.uci.edu/ml. Accessed March 10, 2015
Liu, J., Li, J., Liu, C., Chen, Y.: Discover dependencies from data—a review. IEEE Trans. Knowl Data Eng. 24(2), 251–264 (2012)
Naumann, F.: Data profiling revisited. SIGMOD Rec. 42(4), 40–49 (2013)
Ng, W.: Ordered functional dependencies in relational databases. Inf. Syst. 24(7), 535–554 (1999)
Northwestern University. WikiTables: Public Site (2015). http://downey-n1.cs.northwestern.edu/public. Accessed March 10, 2015
Papenbrock, T., Bergmann, T., Finke, M., Zwiener, J., Naumann, F.: Data profiling with Metanome. Proc. VLDB Endow. 8(12), 1860–1871 (2015)
Papenbrock, T., Ehrlich, J., Marten, J., Neubert, T., Rudolph, J.-P., Schönberg, M., Zwiener, J., Naumann, F.: Functional dependency discovery: An experimental evaluation of seven algorithms. Proc. VLDB Endow. 8(10), 1082–1093 (2015)
Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences—A000522 (2015). http://oeis.org/A000522. Accessed March 10, 2015
Szlichta, J., Godfrey, P., Gryz, J.: Chasing polarized order dependencies. In: Proceedings of the Alberto Mendelzon International Workshop on Foundations of Data Management (AMW), pp. 168–179, (2012)
Szlichta, J., Godfrey, P., Gryz, J.: Fundamentals of order dependencies. Proc. VLDB Endow. 5(11), 1220–1231 (2012)
Szlichta, J., Godfrey, P., Gryz, J., Ma, W., Qiu, W., Zuzarte, C.: Business-intelligence queries with order dependencies in DB2. In: Proceedings of the International Conference on Extending Database Technology (EDBT), pp. 750–761, (2014)
Szlichta, J., Godfrey, P., Gryz, J., Zuzarte, C.: Expressiveness and complexity of order dependencies. Proc. VLDB Endow. 6(14), 1858–1869 (2013)
Acknowledgments
We thank Ziawasch Abedjan for his numerous helpful comments, which improved this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Langer, P., Naumann, F. Efficient order dependency detection. The VLDB Journal 25, 223–241 (2016). https://doi.org/10.1007/s00778-015-0412-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00778-015-0412-3