Vertex Sparsifiers: New Results from Old Techniques

@article{Englert2014VertexSN,
  title={Vertex Sparsifiers: New Results from Old Techniques},
  author={Matthias Englert and A. Gupta and Robert Krauthgamer and Harald R{\"a}cke and Inbal Talgam-Cohen and Kunal Talwar},
  journal={ArXiv},
  year={2014},
  volume={abs/1006.4586}
}
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? Improving on results of Moitra [Proceedings of the 50th IEEE… Expand
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