## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Friday, May 16, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G61

Speaker: Carola Doerr (Laboratoire d'Informatique de Paris 6)

## Computing Point Sets of Low Star Discrepancy with Genetic Algorithms

The star discrepancy of a point set is a measure for its irregularity. Point sets of low star discrepancy value allow Quasi-Monte Carlo integration with small approximation error. Obtaining such point sets is thus one of the classic and well-studied tasks in numerical integration theory. While most research has focused on computing point sets with nice asymptotic behavior, not many constructions are known for optimizing the star discrepancy in fixed dimensions and for a fixed number of points. For all practical purposes, it is thus questionable if the existing constructions are satisfactory. In this talk we will see that indeed there is much room for improvement. We use a simple randomized search heuristic to find point sets that have a star discrepancy value that is much smaller than what theoretical results predict.

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