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Functional Dependencies in Incomplete Databases with Limited Domains

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Foundations of Information and Knowledge Systems (FoIKS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12012))

Abstract

Missing data value is an extensive problem in both research and industrial developers. Two general approaches are there to deal with the problem of missing values in databases, they either could be ignored (removed) or imputed (filled in) with new values [9]. In the present paper, we use the second method. Possible worlds were introduced in [14, 16] and possible and certain keys, as well as weak and strong functional dependencies were studied. We introduced the intermediate concept of strongly possible worlds that are obtained by imputing values already existing in the table in a preceding paper. This results in strongly possible keys and strongly possible functional dependencies. We give a polynomial algorithm to verify a single spKey, and show that in general, it is NP-complete to verify an arbitrary collection of spKeys. We give a graph theoretical characterization of the validity of a given spFD \(X\rightarrow _{sp}Y\). We analyze which weak/strong functional dependency axioms remain sound for strongly possible functional dependencies and give appropriate modifications of the not sound ones.

Research of the second author was partially supported by the National Research, Development and Innovation Office (NKFIH) grant K–116769. This work is also connected to the scientific program of the “Development of quality-oriented and harmonized R+D+I strategy and functional model at BME” project, supported by the New Hungary Development Plan (Project ID: TMOP-4.2.1/B-09/1/KMR-2010-0002).

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Notes

  1. 1.

    Let G(V, E) be a graph and \(L:V\rightarrow 2^{\mathbb {N}}\) be a mapping that assigns each vertex a L(v). A is a mapping \(c:V\rightarrow \bigcup _{v\in V}L(v)\) such that \(c(v)\in L(v)\) and \(c(u)\ne c(v)\) if \(\{u,v\}\in E\).

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Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary

    Munqath Alattar & Attila Sali

  2. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Attila Sali

Authors
  1. Munqath Alattar
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  2. Attila Sali
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Corresponding author

Correspondence to Attila Sali .

Editor information

Editors and Affiliations

  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. University of Helsinki, Helsinki, Finland

    Juha Kontinen

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Alattar, M., Sali, A. (2020). Functional Dependencies in Incomplete Databases with Limited Domains. In: Herzig, A., Kontinen, J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2020. Lecture Notes in Computer Science(), vol 12012. Springer, Cham. https://doi.org/10.1007/978-3-030-39951-1_1

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  • DOI: https://doi.org/10.1007/978-3-030-39951-1_1

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