Roundings Respecting Hard Constraints

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, J. Complexity, 21:691– 709, 2005]. 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 lowdiscrepancy 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. Key words: Star discrepancy, low-discrepancy points, randomized rounding, derandomization

• Type: Conference
• Year: 2005
• Where: STACS
• Authors: Benjamin Doerr
• Keywords: Algorithm, Randomized Rounding, STACS 2005, Star Discrepancy, Theoretical Computer Science