Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Randomized algorithms
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Embeddings of finite metrics
Cuts, Trees and ℓ1-Embeddings of Graphs*
Combinatorica
Embedding k-Outerplanar Graphs into l1
SIAM Journal on Discrete Mathematics
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT
Computational Complexity
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Geometry of Cuts and Metrics
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
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Motivated by applications in combinatorial optimization, we study the extent to which the global properties of a metric space, and especially its embeddability into $\ell_1$ with low distortion, are determined by the properties of its small subspaces. We establish both upper and lower bounds on the distortion of embedding locally constrained metrics into various target spaces. Other aspects of locally constrained metrics are studied as well, in particular, how far are those metrics from general metrics.