Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Mining quantitative association rules in large relational tables
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Beyond market baskets: generalizing association rules to correlations
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Fast discovery of association rules
Advances in knowledge discovery and data mining
Data mining, hypergraph transversals, and machine learning (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Levelwise Search and Borders of Theories in KnowledgeDiscovery
Data Mining and Knowledge Discovery
Discovery of Frequent Episodes in Event Sequences
Data Mining and Knowledge Discovery
Data-Driven Discovery of Quantitative Rules in Relational Databases
IEEE Transactions on Knowledge and Data Engineering
Mining for Empty Rectangles in Large Data Sets
ICDT '01 Proceedings of the 8th International Conference on Database Theory
Fast Algorithms for Mining Association Rules in Large Databases
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Discovery of Multiple-Level Association Rules from Large Databases
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
An Efficient Algorithm for Mining Association Rules in Large Databases
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
Mining Generalized Association Rules
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
Sampling Large Databases for Association Rules
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An Algorithm for Dualization in Products of Lattices and Its Applications
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Mining maximal frequent intervals
Proceedings of the 2003 ACM symposium on Applied computing
An intersection inequality for discrete distributions and related generation problems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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Let ${\mathcal D}$ be a database of transactions on n attributes, where each attribute specifies a (possibly empty) real closed interval $I= [a,b] \subseteq {\mathbb R}$. Given an integer threshold t, a multi-dimensional interval I = ([a1,b1], ..., [an,bn]) is called t-frequent, if (every component interval of) I is contained in (the corresponding component of) at least t transactions of ${\mathcal D}$ and otherwise, I is said to be t-infrequent. We consider the problem of generating all minimalt-infrequent multi-dimensional intervals, for a given database ${\mathcal D}$ and threshold t. This problem may arise, for instance, in the generation of association rules for a database of time-dependent transactions. We show that this problem can be solved in quasi-polynomial time. This is established by developing a quasi- polynomial time algorithm for generating maximal independent elements for a set of vectors in the product of lattices of intervals, a result which may be of independent interest. In contrast, the generation problem for maximal frequent intervals turns out to be NP-hard.