## 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: Thursday, April 10, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Lutz Warnke

## Asymptotic Packing via A Branching Process

Consider a universe of size $n$ with a family of sets, each of size $k$, such that each element is in ~$D$ sets and any two elements have only $o(D)$ common sets. Asymptotics are for fixed $k$ and with $n, D \to \infty$. A subfamily of ~$n/k$ disjoint sets is called an asymptotic optimal packing. The existence of such a packing was shown by Pippenger and Spencer in 1989.

In this talk I will explain a simpler proof from Spencer which analyzes a random greedy algorithm. It is based on establishing a connection between the algorithm and a Poisson birth process.

Paper by Joel Spencer, Asymptotic Packing via A Branching Process, Random Structures and Algorithms 7 (2) (1995).

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