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
Approximation algorithms for the 0-extension problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Lectures on Discrete Geometry
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st 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
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
High-dimensional computational geometry
High-dimensional computational geometry
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Reordering buffers for general metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Inapproximability for Metric Embeddings into R^d
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating edit distance in near-linear time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We initiate the study of on-line metric embeddings. In such an embedding we are given a sequence of n points X = x1, ..., xn one by one, from a metric space M = (X,D). Our goal is to compute a low-distortion embedding of M into some host space, which has to be constructed in an on-line fashion, so that the image of each xi depends only on x1, ..., xi. We prove several results translating existing embeddings to the on-line setting, for the case of embedding into lp spaces, and into distributions over ultrametrics.