06-14   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Benjamin Doerr, Michael Gnewuch:

Construction of low-discrepancy point sets of small size by bracketing covers and dependent randomized rounding

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 algorithm presented for this problem in [B. Doerr, M. Gnewuch, A. Srivastav. Bounds and constructions for the star discrepancy via δ-covers. J. Complexity, 21: 691-709, 2005]. Besides leading to better theoretical run time bounds, our approach can be implemented with reasonable effort.

Mathematics Subject Classification (1991): 11K38

Bibliographical note: Proceedings "Monte Carlo and quasi-Monte Carlo methods 2006", Springer Verlag

Keywords: star discrepancy, dependent randomized rounding, bracketing, derandomization, low-discrepancy point sets

Mail an Jens Burmeister
[Thu Feb 19 18:56:37 2009]