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 Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 10, Pages 1926–1935 (Mi zvmmf9772)

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.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:10, 1472–1481

Bibliographic databases:

UDC: 519.7

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

Citation in format AMSBIB
\Bibitem{DyuSot12} \by E.~V.~Dyukova, R.~M.~Sotnezov \paper On the complexity of the dualization problem \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2012 \vol 52 \issue 10 \pages 1926--1935 \mathnet{http://mi.mathnet.ru/zvmmf9772} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3150300} \zmath{https://zbmath.org/?q=an:1274.68137} \transl \jour Comput. Math. Math. Phys. \yr 2012 \vol 52 \issue 10 \pages 1472--1481 \crossref{https://doi.org/10.1134/S0965542512100090} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. V. Dyukova, P. A. Prokofev, “Ob asimptoticheski optimalnom perechislenii neprivodimykh pokrytii bulevoi matritsy”, PDM, 2014, no. 1(23), 96–105
2. E. V. Djukova, P. A. Prokofjev, “Asymptotically optimal dualization algorithms”, Comput. Math. Math. Phys., 55:5 (2015), 891–905
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