Parameterized exact and approximation algorithms for maximum $k$-set cover and related satisfiability problems

Bonnet, Édouard; Paschos, Vangelis Th.; Sikora, Florian

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 3, pp. 227-240.

Given a family of subsets �� over a set of elements $X$ and two integers $p$ and $k$, max $k$-set cover consists of finding a subfamily �� ⊆ �� of cardinality at most $k$, covering at least $p$ elements of $X$. This problem is W[2]-hard when parameterized by $k$, and FPT when parameterized by $p$. We investigate the parameterized approximability of the problem with respect to parameters $k$ and $p$. Then, we show that max sat-$k$, a satisfiability problem generalizing max $k$-set cover, is also FPT with respect to parameter $p$.

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