Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
The complexity of Boolean functions
The complexity of Boolean functions
On generating all maximal independent sets
Information Processing Letters
Efficient algorithms for listing combinatorial structures
Efficient algorithms for listing combinatorial structures
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Discrete neural computation: a theoretical foundation
Discrete neural computation: a theoretical foundation
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Computing threshold functions by depth-3 threshold circuits with smaller thresholds of their gates
Information Processing Letters
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
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
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
Generating all maximal independent sets of bounded-degree hypergraphs
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Matroid Intersections, Polymatroid Inequalities, and Related Problems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Generating Partial and Multiple Transversals of a Hypergraph
ICALP '00 Proceedings of the 27th 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
On Maximal Frequent and Minimal Infrequent Sets in Binary Matrices
Annals of Mathematics and Artificial Intelligence
Non-uniform Turán-type problems
Journal of Combinatorial Theory Series A
Approximating the number of frequent sets in dense data
Knowledge and Information Systems
On the Complexity of Constraint-Based Theory Extraction
DS '09 Proceedings of the 12th International Conference on Discovery Science
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Given a Boolean matrix and a threshold t, a subset of the columns is frequent if there are at least t rows having a 1 entry in each corresponding position. This concept is used in the algorithmic, combinatorial approach to knowledge discovery and data mining. We consider the complexity aspects of frequent sets. An explicit family of subsets is given that requires exponentially many rows to be represented as the family of frequent sets of a matrix, with any threshold. Examples are given of families that can be represented by a small matrix with threshold t, but that require a significantly larger matrix if the threshold is less than t. We also discuss the connections of these problems to circuit complexity and the existence of efficient listing algorithms.