Mining approximate interval-based temporal dependencies

Temporal functional dependencies add valid time to classical functional dependencies in order to express data integrity constraints over the flow of time. If the temporal dimension adopted is an interval, we have to deal with interval-based temporal functional dependencies (ITFDs for short), which consider different interval relations between tuple valid times. The related approximate problem is when we want to check whether our data satisfy, without any constraint for the schema, a given ITFD under a given error threshold $$0 \leqslant \epsilon \leqslant 1$$0⩽ϵ⩽1. This can be rephrased as: given a relation instance r, is it possible to delete at most $$\epsilon \cdot |r|$$ϵ·|r| tuples from it in such a way that the resulting instance satisfies the given ITFD? This optimization problem, ITFD-Approx for short, may represent a way to discover (i.e., mine) important dependencies among attribute values in a database. In this paper we analyze the complexity of problem ITFD-Approx restricting ourselves to Allen’s interval relations: we shall see how the complexity of such a problem may significantly change, depending on the considered interval relation.

[1]  Jef Wijsen.  Temporal Integrity Constraints , 2009, Encyclopedia of Database Systems.

[2]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[3]  Laks V. S. Lakshmanan,et al.  On approximating optimum repairs for functional dependency violations , 2009, ICDT '09.

[4]  Victor Vianu.  Dynamic functional dependencies and database aging , 1987, JACM.

[5]  Ling Liu,et al.  Encyclopedia of Database Systems , 2009, Encyclopedia of Database Systems.

[6]  Davide Bresolin,et al.  Complete and Terminating Tableau for the Logic of Proper Subinterval Structures Over Dense Orderings , 2009, M4M.

[7]  Davide Bresolin,et al.  Tableaux for Logics of Subinterval Structures over Dense Orderings , 2010, J. Log. Comput..

[8]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[9]  Ronald Fagin,et al.  Database Theory - ICDT 2009, 12th International Conference, St. Petersburg, Russia, March 23-25, 2009, Proceedings , 2009, ICDT.

[10]  Gaëlle Fontaine,et al.  Why is it Hard to Obtain a Dichotomy for Consistent Query Answering? , 2013, 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science.

[11]  Phokion G. Kolaitis,et al.  Repair checking in inconsistent databases: algorithms and complexity , 2009, ICDT '09.

[12]  Jef Wijsen,et al.  Temporal FDs on complex objects , 1999, TODS.

[13]  Jan Chomicki,et al.  Minimal-change integrity maintenance using tuple deletions , 2002, Inf. Comput..

[14]  Jakub Michaliszyn,et al.  The Undecidability of the Logic of Subintervals , 2014, Fundam. Informaticae.

[15]  Pietro Sala,et al.  Mining approximate temporal functional dependencies with pure temporal grouping in clinical databases , 2015, Comput. Biol. Medicine.

[16]  Pietro Sala,et al.  Mining Approximate Temporal Functional Dependencies Based on Pure Temporal Grouping , 2013, 2013 IEEE 13th International Conference on Data Mining Workshops.

[17]  Sushil Jajodia,et al.  Logical design for temporal databases with multiple granularities , 1997, TODS.

[18]  Pietro Sala,et al.  Interval-based temporal functional dependencies: specification and verification , 2013, Annals of Mathematics and Artificial Intelligence.

[19]  Angelo Montanari,et al.  A Uniform Framework for Temporal Functional Dependencies with Multiple Granularities , 2011, SSTD.

[20]  Hannu Toivonen,et al.  Efficient discovery of functional and approximate dependencies using partitions , 1998, Proceedings 14th International Conference on Data Engineering.

[21]  Christian S. Jensen,et al.  Extending Existing Dependency Theory to Temporal Databases , 1996, IEEE Trans. Knowl. Data Eng..

[22]  E. F. Codd,et al.  Normalized Data Structure: A Brief Tutorial. , 1971 .

[23]  E. F. Codd,et al.  Normalized data base structure: a brief tutorial , 1971, SIGFIDET '71.

[24]  Yuval Shahar,et al.  Temporal Information Systems in Medicine , 2010 .

[25]  Heikki Mannila,et al.  On the Complexity of Inferring Functional Dependencies , 1992, Discret. Appl. Math..

[26]  Pietro Sala,et al.  Approximate Interval-Based Temporal Dependencies: The Complexity Landscape , 2014, 2014 21st International Symposium on Temporal Representation and Reasoning.

[27]  Heikki Mannila,et al.  Algorithms for Inferring Functional Dependencies from Relations , 1994, Data Knowl. Eng..

[28]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[29]  Angelo Montanari,et al.  The t4sql temporal query language , 2007, CIKM '07.

[30]  Yde Venema,et al.  A Modal Logic for Chopping Intervals , 1991, J. Log. Comput..

[31]  Sushil Jajodia,et al.  Time Granularities in Databases, Data Mining, and Temporal Reasoning , 2000, Springer Berlin Heidelberg.

[32]  Christian S. Jensen,et al.  Temporal Database , 2009, Encyclopedia of Database Systems.

[33]  Pietro Sala,et al.  Temporal Functional Dependencies Based on Interval Relations , 2011, 2011 Eighteenth International Symposium on Temporal Representation and Reasoning.

[34]  Hannu Toivonen,et al.  TANE: An Efficient Algorithm for Discovering Functional and Approximate Dependencies , 1999, Comput. J..

[35]  Heikki Mannila,et al.  Approximate Inference of Functional Dependencies from Relations , 1995, Theor. Comput. Sci..