A parallel algorithmic version of the Local Lemma
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Decomposing graphs into regions of small diameter
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
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
IDMaps: a global internet host distance estimation service
IEEE/ACM Transactions on Networking (TON)
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
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Constructing internet coordinate system based on delay measurement
Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
Practical, distributed network coordinates
ACM SIGCOMM Computer Communication Review
PIC: Practical Internet Coordinates for Distance Estimation
ICDCS '04 Proceedings of the 24th International Conference on Distributed Computing Systems (ICDCS'04)
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Measured Descent: A New Embedding Method for Finite Metrics
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Triangulation and Embedding Using Small Sets of Beacons
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Journal of the ACM (JACM)
Big-bang simulation for embedding network distances in Euclidean space
IEEE/ACM Transactions on Networking (TON)
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph Augmentation via Metric Embedding
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Combinatorial Framework for Similarity Search
SISAP '09 Proceedings of the 2009 Second International Workshop on Similarity Search and Applications
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
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
Low distortion metric embedding into constant dimension
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Bandwidth and low dimensional embedding
Theoretical Computer Science
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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A fundamental question of metric embedding is whether the metric dimension of a metric space is related to its intrinsic dimension. That is whether the dimension in which it can be embedded in some real normed space is implied by the intrinsic dimension which is reflected by the inherent geometry of the space. The existence of such an embedding was conjectured by Assouad and was later posed as an open problem by others. This question is tightly related to a major goal of many practical application fields: developing tools to represent intrinsically low dimensional metric data sets in a succinct manner. In this paper we give the first algorithmic technique with formal guarantees for finding faithful and low dimensional representations of data lying in high dimensional space. Our main theorem states that every finite metric space X embeds into Euclidean space with dimension O(dim(X)/∈) and distortion O(log 1+εn), where dim(X) is the doubling dimension of the space X. Moreover, we show that X can be embedded into dimension Õ(dim(X)) with constant average distortion and lq-distortion for any q (X) = o(log |X|).