Parameterized algorithms for the max k-set cover and related satisfiability problems

Edouard Bonnet (1) , Vangelis Paschos (1) , Florian Sikora (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

Given a family of subsets S = {S1, . . . , Sm} over a set of elements X = {x1, . . . , xn} and an integer p, max k-set cover consists of finding a set T of at most k subsets covering at least p elements. This problem, when parameterized by k, can be easily shown to be W[2]-hard. Here, we settle the parameterized complexity of max k-set cover under several parameters as max{k,_}, where _ = maxi{|Si|}, p and max{k, f}, where f = maxi |{j|xi 2 Sj}|. We also study parameterized approximability of the problem with respect to parameters k and p. We also study parameterization of a satisfiability problem that is linked to max k-set cover in a sense explained in the paper. Finally, we sketch an enhancement of the classes of the W[*] that seems more appropriate for showing completeness of hard W[*]-problems.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Edouard Bonnet, Vangelis Paschos, Florian Sikora. Parameterized algorithms for the max k-set cover and related satisfiability problems. 2013. ⟨hal-00874259⟩