Characterizations of inner product spaces
Characterizations of inner product spaces
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Lectures on Discrete Geometry
A tight bound on approximating arbitrary metrics by tree metrics
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
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Markov convexity and local rigidity of distorted metrics
Proceedings of the twenty-fourth annual symposium on Computational geometry
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We introduce the notion of metric cotype, a property of metric spaces related to a property of normed spaces, called Rademacher cotype. Apart from settling a long standing open problem in metric geometry, this property is used to prove the following dichotomy: A family of metric spaces F is either almost universal (i.e., contains any finite metric space with any distortion 1), or there exists α 0, and arbitrarily large n-point metrics whose distortion when embedded in any member of F is at least Ω((log n)α). The same property is also used to prove strong non-embeddability theorems of Lq into Lp, when q max{2, p}. Finally we use metric cotype to obtain a new type of isoperimetric inequality on the discrete torus.