## 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: Monday, September 11, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G11

Speaker: Haris Angelidakis (Toyota Technological Institute at Chicago)

## Algorithms for Stable and Perturbation-Resilient Problems

We study a beyond-worst-case-analysis framework known as stability and perturbation resilience, introduced by Bilu and Linial (2010) and Awasthi, Blum, and Sheffet (2012). A combinatorial optimization problem is $\alpha$-stable or $\alpha$-perturbation-resilient if the optimal solution does not change when we perturb all parameters of the problem by a factor of at most $\alpha$. We present improved algorithms for stable instances of clustering problems, such as k-means and k-median, and also give improved algorithms for stable instances of Minimum Multiway Cut. We conclude with several hardness results for stable instances of covering problems. Based on joint work with Konstantin Makarychev and Yury Makarychev.

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