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Mining approximate interval-based temporal dependencies

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Abstract

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 \(0 \leqslant \epsilon \leqslant 1\). This can be rephrased as: given a relation instance r, is it possible to delete at most \(\epsilon \cdot |r|\) 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.

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Notes

  1. A function \(f:{\mathbb {N}}\rightarrow {\mathbb {N}}\) is super-additive if for every pair of elements \(x,y \in {\mathbb {N}}\) we have that \(f(x+y)\geqslant f(x) + f(y)\).

  2. This is the formulation of the problem in its evaluation version and the same assumption made in Sect. 2.2 for \(\sim \)-MaxConsistent holds for Max2Sat too.

  3. Notice that in the terminology of database repairing we have that boldfaced lower-case letters (e.g. \({\mathbf {x}}, {\mathbf {y}}, \ldots \)) denote sets of attributes while lower case letters (e.g. \(x, y, \ldots \)) denote a single attribute.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Carlo Combi & Pietro Sala

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  1. Carlo Combi
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  2. Pietro Sala
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Correspondence to Pietro Sala.

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Ethical statement

Pietro Sala is founded by the Department of Computer Science and the Department of Public Health and Community Medicine, Pharmacology section both of the University of Verona, in the context of the project “An interval-based approach for data analysis and workflow modelling in medical domains”.

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The authors declare that they have no conflict of interest.

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Combi, C., Sala, P. Mining approximate interval-based temporal dependencies. Acta Informatica 53, 547–585 (2016). https://doi.org/10.1007/s00236-015-0246-x

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