How to assign votes in a distributed system
Journal of the ACM (JACM)
Design by exmple: An application of Armstrong relations
Journal of Computer and System Sciences
On generating all maximal independent sets
Information Processing Letters
A fast parallel algorithm for computing all maximal cliques in a graph and the related problems
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Computational learning theory: an introduction
Computational learning theory: an introduction
Exact transversal hypergraphs and application to Boolean &mgr;-functions
Journal of Symbolic Computation
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
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
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
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
A Theory of Coteries: Mutual Exclusion in Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
NP-Completeness: A Retrospective
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
On the Complexity of Some Enumeration Problems for Matroids
SIAM Journal on Discrete Mathematics
A new algorithm for the hypergraph transversal problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On the complexity of monotone dualization and generating minimal hypergraph transversals
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
Lower bounds for three algorithms for the transversal hypergraph generation
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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Given the irredundant CNF representation ϕ of a monotone Boolean function f:{0,1}n{0,1}, the dualization problem calls for finding the corresponding unique irredundant DNF representation ψ of f. The (generalized) multiplication method works by repeatedly dividing the clauses of ϕ into (not necessarily disjoint) groups, multiplying-out the clauses in each group, and then reducing the result by applying the absorption law. We present the first non-trivial upper-bounds on the complexity of this multiplication method. Precisely, we show that if the grouping of the clauses is done in an output-independent way, then multiplication can be performed in sub-exponential time. (n|ψ|)o(radic;|φ|)|φ|O(logn). On the other hand, multiplication can be carried-out in quasi-polynomial time poly (n|ψ|)ċ|ϕ|o(log|ψ|), provided that the grouping is done depending on the intermediate outputs produced during the multiplication process.