English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 193-203

Volume 24, No 2, 2017, P. 87-106

UDC 519.157.1
I. P. Chukhrov
Proof of covering minimality by generalizing the notion of independence

A method is proposed for obtaining lower bounds for the length of the shortest cover and complexity of the minimal cover based on the notion of independent family of sets. For the problem of minimization of Boolean functions, we provide the functions and construct coverings by faces of the set of unit vertices for which the suggested lower bounds can be achieved in the case of five or more variables. The lower bounds, based on independent sets, are unreachable and cannot be used as sufficient conditions for minimality of such functions.
Bibliogr. 11.

Keywords: set covering problem, complexity, shortest cover, minimum cover, independent set, lower bound, condition of minimality.

DOI: 10.17377/daio.2017.24.540

Igor P. Chukhrov 1
1. Institute of Computer Aided Design RAS,
19/18 Vtoraya Brestskaya St., 123056 Moscow, Russia
e-mail: chip@icad.org.ru

Received 27 April 2016
Revised 17 November 2016


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