## 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: Tuesday, March 22, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: May Szedlák

## Random Sampling with Removal

Random sampling is a classical tool in constrained optimization. Under favorable conditions, the optimal solution subject to a small subset of randomly chosen constraints violates only a small subset of the remaining constraints. Here we study the following variant that we call random sampling with removal: suppose that after sampling the subset, we remove a fixed number of constraints from the sample, according to an arbitrary rule. Is it still true that the optimal solution of the reduced sample violates only a small subset of the constraints? We study sampling with removal in so called violator spaces. Using different proof techniques we prove two different upper bounds on the expected number of violators after removal of $k$ elements. For a large range of values of $k$, the new upper bounds improve the previously best bounds for LP-type problems, which moreover had only been known in special cases. This is joint work with Bernd Gärtner and Johannes Lengler.

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