Searching dynamic point sets in spaces with bounded doubling dimension

Authors:
Richard Cole;Lee-Ad Gottlieb
Affiliations:
New York University, New York, NY;New York University, New York, NY
Venue:
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Year:
2006

Citing 11
Cited 22

A randomized algorithm for closest-point queries

SIAM Journal on Computing
A decomposition of multi-dimensional point-sets with applications to k-nearest-neighbors and n-body potential fields (preliminary version)

STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A data structure for dynamically maintaining rooted trees

Journal of Algorithms
An optimal algorithm for approximate nearest neighbor searching fixed dimensions

Journal of the ACM (JACM)
Searching in metric spaces

ACM Computing Surveys (CSUR)
Finding nearest neighbors in growth-restricted metrics

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
Fast construction of nets in low dimensional metrics, and their applications

SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Dynamic LCA Queries on Trees

SIAM Journal on Computing
The black-box complexity of nearest-neighbor search

Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)

Fully dynamic geometric spanners

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Disorder inequality: a combinatorial approach to nearest neighbor search

WSDM '08 Proceedings of the 2008 International Conference on Web Search and Data Mining
Ultra-low-dimensional embeddings for doubling metrics

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
Approximating TSP on metrics with bounded global growth

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Localized Spanner Construction for Ad Hoc Networks with Variable Transmission Range

ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Combinatorial algorithms for nearest neighbors, near-duplicates and small-world design

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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)
Approximation algorithm for the kinetic robust K-center problem

Computational Geometry: Theory and Applications
How to complete a doubling metric

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Localized spanner construction for ad hoc networks with variable transmission range

ACM Transactions on Sensor Networks (TOSN)
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, precise and dynamic distance queries

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
Approximate bregman near neighbors in sublinear time: beyond the triangle inequality

Proceedings of the twenty-eighth annual symposium on Computational geometry
Linear-size approximations to the vietoris-rips filtration

Proceedings of the twenty-eighth annual symposium on Computational geometry
Efficient regression in metric spaces via approximate lipschitz extension

SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a new data structure that facilitates approximate nearest neighbor searches on a dynamic set of points in a metric space that has a bounded doubling dimension. Our data structure has linear size and supports insertions and deletions in O(log n) time, and finds a (1+ε)-approximate nearest neighbor in time O(log n) + (1/ε)O(1). The search and update times hide multiplicative factors that depend on the doubling dimension; the space does not. These performance times are independent of the aspect ratio (or spread) of the points.