## 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, May 27, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Jiří Matoušek (Charles Univ., Prague)

## Low-distortion embeddings in R^d

We consider the problem of embedding a given n-point metric space into the Euclidean space of dimension d, where d is considered fixed (and small). We review worst-case bounds on the required distortion, and we present new results on inapproximability of the minimum distortion by a polynomial-time algorithm. In particular, for d=3 or larger, we show that it is hard to distinguish spaces that admit embedding with a constant distortion from spaces requiring distortion of order n^{const/d}.

Joint work with Anastasios Sidiropoulos.

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