Design by exmple: An application of Armstrong relations
Journal of Computer and System Sciences
Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Dualization of regular Boolean functions
Discrete Applied Mathematics
An O(mn) algorithm for regular set-covering problems
Theoretical Computer Science
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
On generating all maximal independent sets
Information Processing Letters
Computational learning theory: an introduction
Computational learning theory: an introduction
An O(nm)-time algorithm for computing the dual of a regular Boolean function
Discrete Applied Mathematics - Special volume: viewpoints on optimization
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
Polynomial-Time Recognition of 2-Monotonic Positive Boolean Functions Given by an Oracle
SIAM Journal on Computing
On the frequency of the most frequently occurring variable in dual monotone DNFs
Discrete Mathematics
Fast discovery of association rules
Advances in knowledge discovery and data mining
A fast and simple algorithm for identifying 2-monotonic positive Boolean functions
Journal of Algorithms
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
Inner-core and outer-core functions of partially defined Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On frequent sets of Boolean matrices
Annals of Mathematics and Artificial Intelligence
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Dual-Bounded Hypergraphs: Generating Partial and Multiple Transversals
Dual-Bounded Hypergraphs: Generating Partial and Multiple Transversals
Monte-Carlo algorithms for enumeration and reliability problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On Generating All Minimal Integer Solutions for a Monotone System of Linear Inequalities
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
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We consider two natural generalizations of the notion of transversal to a finite hypergraph, arising in data-mining and machine learning, the so called multiple and partial transversals. We show that the hypergraphs of all multiple and all partial transversals are dual- bounded in the sense that in both cases, the size of the dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial transversals of an arbitrary hypergraph are polynomial-time reducible to the well-known dualization problem of hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal Boolean solutions for an arbitrary monotone system of linear inequalities. Thus, it is unlikely that these problems are NP-hard.