# DAN

## Seminar

### Vertex sparsifiers: New results from old techniques (and some open questions)

Seminar Room 1, Newton Institute

#### Abstract

Given a capacitated graph G = (V,E) and a set of terminals $K \subseteq V$, how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flow-sparsifier for G.) What if we want H to be a ``simple'' graph? What if we allow H to be a convex combination of simple graphs? And is the question easier if we wanted H to maintain the distances among the terminals (rather than flows)? Joint work with Matthias Englert, Anupam Gupta, Robert Krauthgamer, Harald Raecke, Inbal Talgam-Cohen and Kunal Talwar.#### Video

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