Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Dualization of regular Boolean functions
Discrete Applied Mathematics
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
Interior and exterior functions of Boolean functions
Discrete Applied Mathematics
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
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
The Maximum Latency and Identification of Positive Boolean Functions
SIAM Journal on Computing
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
Dual-Bounded Generating Problems: Partial and Multiple Transversals of a Hypergraph
SIAM Journal on Computing
Mining Generalized Association Rules
VLDB '95 Proceedings of the 21th 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
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
An inequality for polymatroid functions and its applications
Discrete Applied Mathematics - Submodularity
Discovering interesting holes in data
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
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
Revisiting numerical pattern mining with formal concept analysis
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Given two finite sets of points X, Y in Rn which can be separated by a nonnegative linear function, and such that the componentwise minimum of any two distinct points in X is dominated by some point in Y, we show that |X| = n|Y|. As a consequence of this result, we obtain quasi-polynomial time algorithms for generating all maximal integer feasible solutions for a given monotone system of separable inequalities, for generating all p-inefficient points of a given discrete probability distribution, and for generating all maximal empty hyper-rectangles for a given set of points in Rn. This provides a substantial improvement over previously known exponential algorithms for these generation problems related to Integer and Stochastic Programming, and Data Mining. Furthermore, we give an incremental polynomial time generation algorithm for monotone systems with fixed number of separable inequalities, which, for the very special case of one inequality, implies that for discrete probability distributions with independent coordinates, both p-efficient and p-inefficient points can be separately generated in incremental polynomial time.