On approximating minimum infrequent and maximum frequent sets

Authors:
Mario Boley
Affiliations:
Fraunhofer IAIS, Schloss Birlinghoven, Sankt Augustin, Germany
Venue:
DS'07 Proceedings of the 10th international conference on Discovery science
Year:
2007

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Abstract

The maximum cardinality of a frequent set as well as the minimum cardinality of an infrequent set are important characteristic numbers in frequent (item) set mining. Gunopulos et al. [10] have shown that finding a maximum frequent set is NP-hard. In this paper I show that the minimization problem is also NP-hard. As a next step I investigate whether these problems can be approximated. While a simple greedy algorithm turns out to approximate a minimum infrequent set within a logarithmic factor one can show that there is no such algorithm for the maximization problem.