A global parallel algorithm for the hypergraph transversal problem
Information Processing Letters
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
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
Theoretical Computer Science
A note on systems with max--min and max-product constraints
Fuzzy Sets and Systems
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
Scientific contributions of Leo Khachiyan (a short overview)
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
An intersection inequality for discrete distributions and related generation problems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Left-to-Right Multiplication for Monotone Boolean Dualization
SIAM Journal on Computing
A new algorithm for the hypergraph transversal problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hi-index | 0.00 |
We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. We first show that, for any monotone system of r linear inequalities in n variables, the number of maximal infeasible integer vectors is at most rn times the number of minimal integer solutions to the system. This bound is accurate up to a polylog(r) factor and leads to a polynomial-time reduction of the enumeration problem to a natural generalization of the well-known dualization problem for hypergraphs, in which dual pairs of hypergraphs are replaced by dual collections of integer vectors in a box. We provide a quasi-polynomial algorithm for the latter dualization problem. These results imply, in particular, that the problem of incrementally generating all minimal integer solutions to a monotone system of linear inequalities can be done in quasi-polynomial time.