Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
BIRCH: an efficient data clustering method for very large databases
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Association rules over interval data
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Implementation of Two Semantic Query Optimization Techniques in DB2 Universal Database
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Semantic Compression and Pattern Extraction with Fascicles
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Using Decision Tree Induction for Discovering Holes in Data
PRICAI '98 Proceedings of the 5th Pacific Rim International Conference on Artificial Intelligence: Topics in Artificial Intelligence
Discovering interesting holes in data
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
An Algorithm for Dualization in Products of Lattices and Its Applications
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Query Optimization via Empty Joins
DEXA '02 Proceedings of the 13th International Conference on Database and Expert Systems Applications
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Finding all minimal infrequent multi-dimensional intervals
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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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.