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

  • Conference paper
Monte Carlo and Quasi-Monte Carlo Methods 2006

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 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 also can be implemented with reasonable effort.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Benjamin Doerr

  2. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098, Kiel, Germany

    Michael Gnewuch

Authors
  1. Benjamin Doerr
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  2. Michael Gnewuch
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ulm University, Albert-Einstein-Allee 11, 89069, Ulm, Germany

    Alexander Keller

  2. Department of Computer Science, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Stefan Heinrich

  3. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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Doerr, B., Gnewuch, M. (2008). Construction of Low-Discrepancy Point Sets of Small Size by Bracketing Covers and Dependent Randomized Rounding. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_17

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