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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 10, Pages 1926–1935
(Mi zvmmf9772)
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This article is cited in 2 scientific papers (total in 2 papers)
On the complexity of the dualization problem
E. V. Dyukova, R. M. Sotnezov Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia
Abstract:
The computational complexity of discrete problems concerning the enumeration of solutions is addressed. The concept of an asymptotically efficient algorithm is introduced for the dualization problem, which is formulated as the problem of constructing irreducible coverings of a Boolean matrix. This concept imposes weaker constraints on the number of “redundant” algorithmic steps as compared with the previously introduced concept of an asymptotically optimal algorithm. When the number of rows in a Boolean matrix is no less than the number of columns (in which case asymptotically optimal algorithms for the problem fail to be constructed), algorithms based on the polynomialtime-delay enumeration of “compatible” sets of columns of the matrix is shown to be asymptotically efficient. A similar result is obtained for the problem of searching for maximal conjunctions of a monotone Boolean function defined by a conjunctive normal form.
Key words:
complexity of enumeration problems, dualization problem, maximal conjunction, irreducible covering of a Boolean matrix, polynomial-time-delay algorithm, asymptotically optimal algorithm of searching for irreducible coverings, metric properties of a set of coverings, metric properties of disjunctive normal forms.
Received: 14.03.2012
Citation:
E. V. Dyukova, R. M. Sotnezov, “On the complexity of the dualization problem”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1926–1935; Comput. Math. Math. Phys., 52:10 (2012), 1472–1481
Linking options:
https://www.mathnet.ru/eng/zvmmf9772 https://www.mathnet.ru/eng/zvmmf/v52/i10/p1926
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Abstract page: | 291 | Full-text PDF : | 80 | References: | 42 | First page: | 18 |
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