## 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, April 19, 2016, 12:15 pm

Duration: 45 minutes

Location: CAB G51

Speaker: Asier Mujika

## Practical Algorithms for Generating a Random Ordering of the Elements of a Weighted Set

Choosing a permutation of n elements uniformly at random is a well-known problem, and it is a simple exercise to design an algorithm which achieves this in time O(n). One natural generalization of the problem is to give weights to the elements, and then draw a permutation based on the distribution induced by these weights, where elements with higher weights are more likely to be at the beginning. In this presentation we will overview existing algorithms for this problem, and describe some new approaches. Even though an algorithm that runs in time O(n) is known, it is fairly complicated. On the other hand, we will see a much simpler algorithm which runs in time O(n log log n) (and is actually possible to implement!) and even O(n) under some restrictions. All in all, we will see some neat algorithm design tricks.

Information for students and suggested topics for student talks