## 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 20, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Anastasios Sidiropoulos (MIT)

## Circular Partitions with Applications to Visualization and Embeddings

We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small aspect ratio, and satisfying specified volume constraints. We apply these partitions to obtain a natural extension of the popular Treemap visualization method. Our proposed algorithm is not constrained in using only rectangles, and can achieve provably better guarantees on the aspect ratio of the constructed polygons.

We also use these partitions to obtain improved approximation algorithms for embedding ultrametrics into d-dimensional Euclidean space. In particular, we give a polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion (Delta denotes the ratio of the maximum over the minimum distance). The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Joint work with Krzysztof Onak.

Information for students and suggested topics for student talks