Abstract
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 \(\textsc{max $k$-vertex cover}{} \notin \textbf{FPT}\) with respect to parameter k unless \(\textbf{FPT} = \textbf{W[1]}\)), 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.
Research supported by the French Agency for Research under the program TODO, ANR-09-EMER-010 and by a Lagrange fellowship of the Fondazione CRT, Torino, Italy.
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Della Croce, F., Paschos, V.T. (2012). Efficient Algorithms for the max k -vertex cover Problem. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_21
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