Abstract
We say, that a database relation represents a Sperner system K on the set of attributes, if the system of minimal keys is exactly K. It is known, that such a representation always exsists. In this paper we show, that the maximum of the minimal number of tuples, that are needed to represent a Sperner system of only two element sets is 3(n/3+o(n)). We consider this problem for other classes of Sperner systems (e.g for the class of trees, i.e. each minimal key has cardinality two, and the keys form a tree), too.
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Tichler, K. (2002). Extremal Theorems for Databases. In: Eiter, T., Schewe, KD. (eds) Foundations of Information and Knowledge Systems. FoIKS 2002. Lecture Notes in Computer Science, vol 2284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45758-5_13
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DOI: https://doi.org/10.1007/3-540-45758-5_13
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