## 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, October 09, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Yves Brise

## On the Autocorrelation of Sets of Disks

We consider a collection of $n$ disjoint disks in $\mathbb{R}^1$ or $\mathbb{R}^2$. We are interested in the so called autocorrelation of this collection, which is the intersection area of the disks with a copy of themselves, if we translate the copy by a vector $t$. Obviously, the autocorrelation is a function in $t$. The concept of autocorrelation has applications mainly in interferometry and signal processing.

The general optimization problem that we are investigating, consists of resizing the disks in such a way that the autocorrelation function is always greater than a given threshold $\mu$, for a given range of $t$. The measure of optimality is just the sum of the radii of the disks, which we want to minimize.

In this talk, I present polynomial time algorithms for some simplified variants of the above problem, and I will discuss some (partial) results about the hardness of the general problem.

Joint work with Bernd Gärtner, Trung Nguyen.

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