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
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 УredundantФ 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 УcompatibleФ 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.
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.
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Computational Mathematics and Mathematical Physics, 2012, 52:10, 1472–1481
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
Citation in format AMSBIB
\by E.~V.~Dyukova, R.~M.~Sotnezov
\paper On the complexity of the dualization problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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E. V. Dyukova, P. A. Prokofev, “Ob asimptoticheski optimalnom perechislenii neprivodimykh pokrytii bulevoi matritsy”, PDM, 2014, no. 1(23), 96–105
E. V. Djukova, P. A. Prokofjev, “Asymptotically optimal dualization algorithms”, Comput. Math. Math. Phys., 55:5 (2015), 891–905
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