Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Approximation algorithms for the 0-extension problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Dimension reduction for ultrametrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Local embeddings of metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Local Global Tradeoffs in Metric Embeddings
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Dimensionality reduction: beyond the Johnson-Lindenstrauss bound
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A nonlinear approach to dimension reduction
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We study the problem of embedding metric spaces into low dimensional lp spaces while faithfully preserving distances from each point to its k nearest neighbors. We show that any metric space can be embedded into [EQUATION] with k-local distortion of O ((log k)/p). We also show that any ultrametric can be embedded into [EQUATION] with k-local distortion 1 + ε. Our embedding results have immediate applications to local Distance Oracles. We show how to preprocess a graph in polynomial time to obtain a data structure of O(nk1/t log2 k) bits, such that distance queries from any node to its k nearest neighbors can be answered with stretch O(t).