Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
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
Disorder inequality: a combinatorial approach to nearest neighbor search
WSDM '08 Proceedings of the 2008 International Conference on Web Search and Data Mining
Embedding metric spaces in their intrinsic dimension
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved algorithms for fully dynamic geometric spanners and geometric routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Computing the Greedy Spanner in Near-Quadratic Time
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Space-Time Tradeoffs for Proximity Searching in Doubling Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Optimal Dynamic Spanner for Doubling Metric Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Combinatorial algorithms for nearest neighbors, near-duplicates and small-world design
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Using the doubling dimension to analyze the generalization of learning algorithms
Journal of Computer and System Sciences
Algorithms for graphs of bounded treewidth via orthogonal range searching
Computational Geometry: Theory and Applications
Space-time tradeoffs for approximate nearest neighbor searching
Journal of the ACM (JACM)
Combinatorial Framework for Similarity Search
SISAP '09 Proceedings of the 2009 Second International Workshop on Similarity Search and Applications
Maintaining Nets and Net Trees under Incremental Motion
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
Recovering the long-range links in augmented graphs
Theoretical Computer Science
Bounded-hop energy-efficient broadcast in low-dimensional metrics via coresets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Small worlds as navigable augmented networks: model, analysis, and validation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
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
Beating the spread: time-optimal point meshing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Low-interference networks in metric spaces of bounded doubling dimension
Information Processing Letters
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate nearest neighbor search for low dimensional queries
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
New constructions of SSPDs and their applications
Computational Geometry: Theory and Applications
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
A new approach to output-sensitive voronoi diagrams and delaunay triangulations
Proceedings of the twenty-ninth annual symposium on Computational geometry
A fast algorithm for well-spaced points and approximate delaunay graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Net and prune: a linear time algorithm for euclidean distance problems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Optimal euclidean spanners: really short, thin and lanky
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Output-sensitive well-separated pair decompositions for dynamic point sets
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Efficient regression in metric spaces via approximate lipschitz extension
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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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.