Data structures and algorithms for nearest neighbor search in general metric spaces
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth 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
Linear-size approximate voronoi diagrams
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Near Neighbor Search in Large Metric Spaces
VLDB '95 Proceedings of the 21th International Conference on Very Large Data Bases
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
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The black-box complexity of nearest-neighbor search
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Algorithms on negatively curved spaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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We consider approximate nearest neighbor searching in metric spaces of constant doubling dimension. More formally, we are given a set Sof npoints and an error bound 茂戮驴 0. The objective is to build a data structure so that given any query point qin the space, it is possible to efficiently determine a point of Swhose distance from qis within a factor of (1 + 茂戮驴) of the distance between qand its nearest neighbor in S. In this paper we obtain the following space-time tradeoffs. Given a parameter 茂戮驴茂戮驴 [2,1/茂戮驴], we show how to construct a data structure of space $n \gamma^{O(\dim)} \log(1/\varepsilon)$ space that can answer queries in time $O(\log(n\gamma)) + (1/(\varepsilon \gamma))^{O(\dim)}$. This is the first result that offers space-time tradeoffs for approximate nearest neighbor queries in doubling spaces. At one extreme it nearly matches the best result currently known for doubling spaces, and at the other extreme it results in a data structure that can answer queries in time O(log(n/茂戮驴)), which matches the best query times in Euclidean space. Our approach involves a novel generalization of the AVD data structure from Euclidean space to doubling space.