# Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, May 20, 2008, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**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.

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