Computing the largest empty rectangle
SIAM Journal on Computing
A note on finding a maximum empty rectangle
Discrete Applied Mathematics
Complexity of identification and dualization of positive Boolean functions
Information and Computation
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
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
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
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Lower bounds for three algorithms for transversal hypergraph generation
Discrete Applied Mathematics
A Fast and Simple Parallel Algorithm for the Monotone Duality Problem
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Left-to-Right Multiplication for Monotone Boolean Dualization
SIAM Journal on Computing
Hi-index | 5.23 |
We show that |X|@?n|Y| must hold for two finite sets X,Y@?R^n whenever they can be separated by a nonnegative linear function such that X is above Y and the componentwise minimum of any two distinct points in X is dominated by some point in Y. As a consequence, we obtain an incremental quasi-polynomial time algorithm 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 hyper-rectangles which contain a specified fraction of points of a given set in R^n. This provides a substantial improvement over previously known exponential time 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, implying that for discrete probability distributions with independent coordinates, both p-efficient and p-inefficient points can be separately generated in incremental polynomial time.