Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE 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
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete & Computational Geometry
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Name independent routing for growth bounded networks
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Small hop-diameter sparse spanners for doubling metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Optimal-stretch name-independent compact routing in doubling metrics
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A doubling dimension threshold θ(loglogn) for augmented graph navigability
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Ultra-low-dimensional embeddings for doubling metrics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating TSP on metrics with bounded global growth
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
How to complete a doubling metric
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Fast approximation in subspaces by doubling metric decomposition
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximate bregman near neighbors in sublinear time: beyond the triangle inequality
Proceedings of the twenty-eighth annual symposium on Computational geometry
Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate nearest neighbor search, well-separated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near-linear and the space being used is linear.