On algorithms for construction of all irreducible partial covers

Authors:
Mikhail Ju. Moshkov
Affiliations:
Institute of Computer Science, University of Silesia, 39, Bedzińska St., Sosnowiec 41-200, Poland
Venue:
Information Processing Letters
Year:
2007

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Abstract

Lower and upper bounds on the cardinality and the number of irreducible partial covers for almost all set cover problems are obtained. These bounds allow us to prove that there is no polynomial algorithm which for almost all set cover problems constructs all irreducible partial covers, but there exists a totally polynomial algorithm which constructs all irreducible partial covers for almost all set cover problems.