A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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
An improved approximation algorithm for the 0-extension problem
SODA '03 Proceedings of the fourteenth 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
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
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
PIC: Practical Internet Coordinates for Distance Estimation
ICDCS '04 Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS'04)
Triangulation and Embedding Using Small Sets of Beacons
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
A duality view of spectral methods for dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
Ramsey partitions and proximity data structures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On low dimensional local embeddings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Combinatorial Framework for Similarity Search
SISAP '09 Proceedings of the 2009 Second International Workshop on Similarity Search and Applications
Depth of field and cautious-greedy routing in social networks
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
Dimensionality reduction: beyond the Johnson-Lindenstrauss bound
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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In many application areas, complex data sets are often representedby some metric space and metric embedding is used to provide a more structured representation of the data. In many of these applications much greater emphasis is put on the preserving the local structure of the original space than on maintaining its complete structure. This is also the case in some networking applications where "small world" phenomena in communication patterns has been observed. Practical study of embedding has indeed involved with finding embeddings with this property. In this paper we initiate thestudy of local embeddings of metric spaces and provide embeddings with distortion depending solely on the local structureof the space.