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Construction of Low-discrepancy Point Sets of Small Size by Bracketing Covers and Dependent Randomized Rounding

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44338

Doerr,  Benjamin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Doerr, B., & Gnewuch, M.(2006). Construction of Low-discrepancy Point Sets of Small Size by Bracketing Covers and Dependent Randomized Rounding (06-14). Kiel: University Kiel.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0019-E49F-6
Abstract
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 -covers. J. Complexity, 21: 691-709, 2005]. Besides leading to better theoretical run time bounds, our approach can be implemented with reasonable effort.