Algorithmic construction of low-discrepancy point sets via dependent randomized rounding

Authors:
Benjamin Doerr;Michael Gnewuch;Magnus Wahlström
Affiliations:
Max-Planck-Institut für Informatik, Campus E1 4, 66123 Saarbrücken, Germany;Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany and Department of Computer Science, Columbia University, 1214 Amsterdam ...;Max-Planck-Institut für Informatik, Campus E1 4, 66123 Saarbrücken, Germany
Venue:
Journal of Complexity
Year:
2010

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Abstract

We provide a deterministic algorithm that constructs small point sets exhibiting a low star discrepancy. The algorithm is based on recent results on randomized roundings respecting hard constraints and their derandomization. It is structurally much simpler than a previous algorithm presented for this problem in [B. Doerr, M. Gnewuch, A. Srivastav, Bounds and constructions for the star discrepancy via @d-covers, J. Complexity, 21 (2005) 691-709]. Besides leading to better theoretical running time bounds, our approach also can be implemented with reasonable effort. We implemented this algorithm and performed numerical comparisons with other known low-discrepancy constructions. The experiments take place in dimensions ranging from 5 to 21 and indicate that our algorithm leads to superior results if the dimension is relatively high and the number of points that have to be constructed is rather small.