Michael Gnewuch

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Tractability of multivariate problems has become nowadays a popular research subject. Polynomial tractability means that the solution of a d-variate problem can be solved to within ε with polynomial cost in ε −1 and d. Unfortunately, many multivariate problems are not polynomially tractable. This holds for all non-trivial unweighted linear tensor product(More)
—Motivated by neutrality observed in natural evolution often redundant encodings are used in evolutionary algorithms. Many experimental studies have been carried out on this topic. In this paper we present a first rigorous runtime analysis on the effect of using neutrality. We consider a simple model where a layer of constant fitness is distributed in the(More)
We continue the study of generalized tractability initiated in our previous paper " Generalized tractability for multivariate problems, Part I: Linear tensor product problems and linear information " , J. Complexity, 23, 262-295 (2007). We study linear tensor product problems for which we can compute linear information which is given by arbitrary continuous(More)
For numerical integration in higher dimensions, bounds for the star-discrepancy with polynomial dependence on the dimension d are desirable. Furthermore , it is still a great challenge to give construction methods for low-discrepancy point sets. In this paper we give upper bounds for the star-discrepancy and its inverse for subsets of the d-dimensional unit(More)
In memory of our friend, colleague and former fellow student Manfred Schocker Summary. We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on bracketing and on recent results on randomized roundings respecting hard constraints. It is structurally much simpler than the previous(More)
We investigate the problem of constructing small point sets with low star discrepancy in the s-dimensional unit cube. The size of the point set shall always be polynomial in the dimension s. Our particular focus is on extending the dimension of a given low-discrepancy point set. This results in a deterministic algorithm that constructs N-point sets with(More)
We construct explicit δ-bracketing covers with minimal cardinality for the set system of (anchored) rectangles in the two dimensional unit cube. More precisely, the cardinality of these δ-bracketing covers are bounded from above by δ −2 +o(δ −2). A lower bound for the cardinality of arbitrary δ-bracketing covers for d-dimensional anchored boxes from [M.(More)
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028–2042] it is based on the optimization algorithm threshold accepting. Our improvements include, amongst others, a non-uniform sampling strategy which is more(More)