How to assign votes in a distributed system
Journal of the ACM (JACM)
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
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
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
Local and Global Methods in Data Mining: Basic Techniques and Open Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
NP-Completeness: A Retrospective
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Hypergraph Transversal Computation and Related Problems in Logic and AI
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
On Maximal Frequent and Minimal Infrequent Sets in Binary Matrices
Annals of Mathematics and Artificial Intelligence
On the Complexity of Some Enumeration Problems for Matroids
SIAM Journal on Discrete Mathematics
On the complexity of the multiplication method for monotone CNF/DNF dualization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Enumerating spanning and connected subsets in graphs and matroids
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Theoretical Computer Science
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
On the complexity of monotone dualization and generating minimal hypergraph transversals
Discrete Applied Mathematics
Deciding monotone duality and identifying frequent itemsets in quadratic logspace
Proceedings of the 32nd symposium on Principles of database systems
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We consider the monotone duality problem i.e., checking whether given monotone CNF φ and DNF *** are equivalent, which is a prominent open problem in NP-completeness. We construct a fast and simple parallel algorithms for the problem, that run in polylogarithmic time by using quasi-polynomially many processors. The algorithm exhibits better parallel time complexity of the existing algorithms of Elbassioni [11]. By using a different threshold of the degree parameter *** of φ in the algorithm, we also present a stronger bound on the number of processors for polylogarithmic-time parallel computation and improves over the previously best known bound on the sequential time complexity of the problem in the case when the magnitudes of |φ |, |*** | and n are different, e.g., |*** | = |φ | *** *** n for *** 1, where n denotes the number of variables. Furthermore, we show that, for several interesting well-known classes of monotone CNFs φ such as bounded degree, clause-size, and intersection-size, our parallel algorithm runs polylogarithmic time by using polynomially many processors.