Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Lectures on Discrete Geometry
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Eigenvalue bounds, spectral partitioning, and metrical deformations via flows
Journal of the ACM (JACM)
Genus and the geometry of the cut graph
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
On the hardness of embeddings between two finite metrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Embedding bounded bandwidth graphs into ℓ1
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Sparsest cut on bounded treewidth graphs: algorithms and hardness results
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We introduce and study the notion of the average distortion of a nonexpanding embedding of one metric space into another. Less sensitive than the multiplicative metric distortion, the average distortion captures well the global picture, and, overall, is a quite interesting new measure of metric proximity, related to the concentration of measure phenomenon. We establish close mutual relations between the MinCut- MaxFlow gap in a uniform-demand multicommodity flow, and the average distortion of embedding the suitable (dual) metric into l1. These relations are exploited to show that the shortest-path metrics of special (e.g., planar, bounded treewidth, etc.) graphs embed into l1 with constant average distortion. The main result of the paper claims that this remains true even if l1 is replaced with the line. This result is further sharpened for graphs of a bounded treewidth.