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

Date:
Monday 10th January 2011 - 11:30 to 12:30
Venue:
INI Seminar Room 1
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.
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