Coarse Differentiation and Multi-flows in Planar Graphs

Authors:
James R. Lee;Prasad Raghavendra
Affiliations:
University of Washington,;University of Washington,
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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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 differentiationin order to lower bound the distortion for embedding a particular family of shortest-path metrics into L1.