Efficient Algorithms for the max k -vertex cover Problem

Federico Della Croce , Vangelis Paschos (1)

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

We first devise moderately exponential exact algorithms for max k -vertex cover, with time-complexity exponential in n but with polynomial space-complexity by developing a branch and reduce method based upon the measure-and-conquer technique. We then prove that, there exists an exact algorithm for max k -vertex cover with complexity bounded above by the maximum among c k and γ τ , for some γ < 2, where τ is the cardinality of a minimum vertex cover of G (note that \textsc{maxk-vertex cover}{} \notin \textbf{FPT} with respect to parameter k unless FPT=W[1] ), using polynomial space. We finally study approximation of max k -vertex cover by moderately exponential algorithms. The general goal of the issue of moderately exponential approximation is to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-case running times importantly smaller than those needed for exact computation, approximation ratios unachievable in polynomial time.

Mots clés: max k -vertex cover

Domaines: Informatique [cs]

Federico Della Croce, Vangelis Paschos. Efficient Algorithms for the max k -vertex cover Problem. 7th International Conference on Theoretical Computer Science (TCS), Sep 2012, Amsterdam, Netherlands. pp.295-309, ⟨10.1007/978-3-642-33475-7_21⟩. ⟨hal-01511883⟩