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We present a new algorithm for estimating the star discrepancy of arbitrarypoint sets. Similar to the algorithm for discrepancy approximation of Winkerand Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on theoptimization algorithm threshold accepting. Our improvements include, amongstothers, a non-uniform sampling strategy which is more suited forhigher-dimensional inputs, and rounding steps which transform axis-parallelboxes, on which the discrepancy is to be tested, into \emph{critical testboxes}. These critical test boxes provably yield higher discrepancy values, andcontain the box that exhibits the maximum value of the local discrepancy. Weprovide comprehensive experiments to test the new algorithm. Our randomizedalgorithm computes the exact discrepancy frequently in all cases where this canbe checked (i.e., where the exact discrepancy of the point set can be computedin feasible time). Most importantly, in higher dimension the new method behavesclearly better than all previously known methods.

A Randomized Algorithm Based on Threshold Accepting to Approximate the Star Discrepancy