Abstract
Many data mining approaches focus on the discovery of similar (and frequent) data values in large data sets. We present an alternative, but complementary approach in which we search for empty regions in the data. We consider the problem of finding all maximal empty rectangles in large, two-dimensional data sets. We introduce a novel, scalable algorithm for finding all such rectangles. The algorithm achieves this with a single scan over a sorted data set and requires only a small bounded amount of memory. We also describe an algorithm to find all maximal empty hyper-rectangles in a multi-dimensional space. We consider the complexity of this search problem and present new bounds on the number of maximal empty hyper-rectangles. We briefly overview experimental results obtained by applying our algorithm to a synthetic data set.
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Edmonds, J., Gryz, J., Liang, D., Miller, R.J. (2001). Mining for Empty Rectangles in Large Data Sets. In: Van den Bussche, J., Vianu, V. (eds) Database Theory — ICDT 2001. ICDT 2001. Lecture Notes in Computer Science, vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44503-X_12
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DOI: https://doi.org/10.1007/3-540-44503-X_12
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