一种基于阈值接受的星离散逼近随机算法
A Randomized Algorithm Based on Threshold Accepting to Approximate the Star Discrepancy
摘要：
提出了一种新的估计任意点集的星差的算法。类似于Winker和Fang [SIAM J. Numer. Anal. 34（1997），2028- 2042]它是基于最优化算法阈值接受。我们的改进包括，除其他外，一个非均匀的采样策略，这是更适合于更高的维度的输入，和四舍五入的步骤，转换轴平行的盒子，其中的差异是要测试，到\emph{critical test boxes}。这些关键测试盒可证明产生更高的差异值，并包含显示局部差异最大值的盒。我们提供了全面的实验来测试新算法。我们的随机算法在可以检查的所有情况下频繁地计算精确的差异（即，其中可以在可行时间内计算点集的精确差异）。最重要的是，在更高的维度，新方法的行为明显优于所有以前已知的方法。
英文摘要：
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization algorithm threshold accepting. Our improvements include, amongst others, a non-uniform sampling strategy which is more suited for higher-dimensional inputs, and rounding steps which transform axis-parallel boxes, on which the discrepancy is to be tested, into \emph{critical test boxes}. These critical test boxes provably yield higher discrepancy values, and contain the box that exhibits the maximum value of the local discrepancy. We provide comprehensive experiments to test the new algorithm. Our randomized algorithm computes the exact discrepancy frequently in all cases where this can be checked (i.e., where the exact discrepancy of the point set can be computed in feasible time). Most importantly, in higher dimension the new method behaves clearly better than all previously known methods.
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