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
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Approximating the bandwidth via volume respecting embeddings (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth 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
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
On the impossibility of dimension reduction in l1
Journal of the ACM (JACM)
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Markov convexity and local rigidity of distorted metrics
Proceedings of the twenty-fourth annual symposium on Computational geometry
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Bandwidth and low dimensional embedding
Theoretical Computer Science
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(MATH) We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than $\Omega(\sqrt\log n\,)$. This matches Rao's general upper bound for metric embedding of planar graphs into Euclidean space, [14], thus resolving the question of how well do planar metrics embed in Euclidean spaces.