Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
On sparse spanners of weighted graphs
Discrete & Computational Geometry
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
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On metric ramsey-type phenomena
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Embeddings of finite metrics
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Reconstructing approximate tree metrics
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Markov convexity and local rigidity of distorted metrics
Proceedings of the twenty-fourth annual symposium on Computational geometry
Online, Dynamic, and Distributed Embeddings of Approximate Ultrametrics
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Motivated by applications in combinatorial optimization, we initiate a study of the extent to which the global properties of a metric space (especially, embeddability in l1 with low distortion) are determined by the properties of small subspaces. We note connections to similar issues studied already in Ramsey theory, complexity theory (especially PCPs), and property testing. We prove both upper bounds and lower bounds on the distortion of embedding locally constrained metrics into various target spaces.