Mining for Empty Rectangles in Large Data Sets

  • Jeff Edmonds
  • Jarek Gryz
  • Dongming Liang
  • Renée J. Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1973)


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.


Association Rule Scalable Algorithm High Step Empty Region Empty Rectangle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jeff Edmonds
    • 1
  • Jarek Gryz
    • 1
  • Dongming Liang
    • 1
  • Renée J. Miller
    • 2
  1. 1.York UniversityUSA
  2. 2.University of Toronto

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