## 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, January 13, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Dieter Mitsche

## The Hidden Cluster Problem

The Hidden Cluster Problem on a random graph is defined as follows: given a graph randomly drawn from a distribution G(n,k,p,q) - a graph on n vertices with k clusters, where p denotes the probability of an edge between two vertices within the same cluster, q denotes the probability of an edge between two vertices in different clusters, p > q - the problem is to find the ('hidden') clusters planted in this graph via this distribution.

In this talk, I will sketch Frank McSherry's approach of solving this problem - in his paper "Spectral Partitioning of Random Graphs' he puts two vertices into the same cluster, if the norm of the difference between the columns in the projection matrix corresponding to these vertices is small.

Frank McSherry, Spectral Partitioning of Random Graphs, Proceedings of 42nd IEEE Symosium on Foundations of Computer Science (FOCS) 201, p. 529-537.

Information for students and suggested topics for student talks