A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Triangulation and Embedding Using Small Sets of Beacons
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sampling in dynamic data streams and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Small space representations for metric min-sum k-clustering and their applications
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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We study the problem of computing low-distortion embeddings in the streaming model. We present streaming algorithms that, given an n -point metric space M , compute an embedding of M into an n -point metric space M *** that preserves a (1 *** *** )-fraction of the distances with small distortion (*** is called the slack ). Our algorithms use space polylogarithmic in n and the spread of the metric. Within such space limitations, it is impossible to store the embedding explicitly. We bypass this obstacle by computing a compact representation of M ***, without storing the actual bijection from M into M ***.