Abstract
We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2. This improves the largest known gap for planar graphs from \(\frac32\) to 2. Our approach uses a technique from geometric group theory called coarse differentiation in order to lower bound the distortion for embedding a particular family of shortest-path metrics into L 1.
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Lee, J.R., Raghavendra, P. (2007). Coarse Differentiation and Multi-flows in Planar Graphs. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_17
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DOI: https://doi.org/10.1007/978-3-540-74208-1_17
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