Computing the largest empty rectangle
SIAM Journal on Computing
Computational learning theory: an introduction
Computational learning theory: an introduction
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
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
Mining quantitative association rules in large relational tables
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
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
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
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Dual-Bounded Generating Problems: Partial and Multiple Transversals of a Hypergraph
SIAM Journal on Computing
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
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Discovering interesting holes in data
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
An intersection inequality for discrete distributions and related generation problems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A note on systems with max--min and max-product constraints
Fuzzy Sets and Systems
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Combinatorial optimization in system configuration design
Automation and Remote Control
Towards a Scalable Query Rewriting Algorithm in Presence of Value Constraints
Journal on Data Semantics XII
Masking patterns in sequences: A new class of motif discovery with don't cares
Theoretical Computer Science
Latticized linear optimization on the unit interval
IEEE Transactions on Fuzzy Systems
Fuzzy Optimization and Decision Making
How to apply SAT-solving for the equivalence test of monotone normal forms
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Enumeration of minimal dominating sets and variants
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Conjunctive query answering in the description logic SH using knots
Journal of Computer and System Sciences
Proceedings of the 2004 European conference on Constraint-Based Mining and Inductive Databases
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Given a finite set V, and a hypergraph H ⊆ 2V, the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for H. This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618-628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.More generally, we consider a monotone property π over a bounded n-dimensional integral box. As an important application of the above hypergraph transversal problem, pioneered by Bioch and Ibaraki [Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 50-63], we consider the problem of incrementally generating simultaneously all minimal subsets satisfying π and all maximal subsets not satisfying π, for properties given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time via a polynomial-time reduction to a generalization of the hypergraph transversal problem on integer boxes. In this paper we present an efficient implementation of this procedure, and present experimental results to evaluate our implementation for a number of interesting monotone properties π.