17 citations · 29 across the 4 of their papers we have counts for
4 papers
Discrepancy Bounds for a Class of Negatively Dependent Random Points Including Latin Hypercube Samples
Michael Gnewuch, Nils Hebbinghaus
We introduce a class of -negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin…
On Negatively Dependent Sampling Schemes, Variance Reduction, and Probabilistic Upper Discrepancy Bounds
Michael Gnewuch, Marcin Wnuk, Nils Hebbinghaus
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlyin…
Discrepancy of Sums of two Arithmetic Progressions
Nils Hebbinghaus
Estimating the discrepancy of the hypergraph of all arithmetic progressions in the set $[N]=\{1,2,\hdots,N\}$ was one of the famous open problems in combinatorial discrepancy theor…
Improved Bounds and Schemes for the Declustering Problem
Benjamin Doerr, Nils Hebbinghaus, Sören Werth
The declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed on the devices. Usi…