On generating all maximal independent sets
Information Processing Letters
Cause-effect relationships and partially defined Boolean functions
Annals of Operations Research
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Complexity of identification and dualization of positive Boolean functions
Information and Computation
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
Dualization, decision lists and identification of monotone discrete functions
Annals of Mathematics and Artificial Intelligence
Generating Partial and Multiple Transversals of a Hypergraph
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
An Incremental RNC Algorithm for Generating All Maximal Independent Sets in Hypergraphs of Bounded Dimension
Matroid Intersections, Polymatroid Inequalities, and Related Problems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On Dualization in Products of Forests
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
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We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. We first show that for any monotone system of r linear inequalities in n variables, the number of maximal infeasible integer vectors is at most rntimes the number of minimal integer solutions to the system. This bound is accurate up to a polylog(r) factor and leads to a polynomial-time reduction of the enumeration problem to a natural generalization of the well-known dualization problem for hypergraphs, in which dual pairs of hypergraphs are replaced by dual collections of integer vectors in a box. We provide a quasi-polynomial algorithm for the latter dualization problem. These results imply, in particular, that the problem of incrementally generating minimal integer solutions of a monotone system of linear inequalities can be done in quasi-polynomial time.