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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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Proceedings of the eighteenth annual symposium on Computational geometry
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Proceedings of the eighteenth annual symposium on Computational geometry
Linear-size approximate voronoi diagrams
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Nearest Neighbors Can Be Found Efficiently If the Dimension Is Small Relative to the Input Size
ICDT '03 Proceedings of the 9th International Conference on Database Theory
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Hausdorff distance under translation for points and balls
Proceedings of the nineteenth annual symposium on Computational geometry
Approximate Nearest Neighbor under edit distance via product metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Space-time tradeoffs for approximate spherical range counting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Entropy based nearest neighbor search in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
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On the importance of idempotence
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)
Lower bounds on locality sensitive hashing
Proceedings of the twenty-second annual symposium on Computational geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Journal of Computer and System Sciences
Nearest-neighbor-preserving embeddings
ACM Transactions on Algorithms (TALG)
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Communications of the ACM - 50th anniversary issue: 1958 - 2008
Fast dimension reduction using Rademacher series on dual BCH codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Spanning Tree with Neighborhoods
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Outlier Detection Based on Voronoi Diagram
ADMA '08 Proceedings of the 4th international conference on Advanced Data Mining and Applications
Dense Fast Random Projections and Lean Walsh Transforms
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Space-Time Tradeoffs for Proximity Searching in Doubling Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Approximate line nearest neighbor in high dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximate voronoi cell computation on spatial data streams
The VLDB Journal — The International Journal on Very Large Data Bases
Quality and efficiency in high dimensional nearest neighbor search
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
Space-time tradeoffs for approximate nearest neighbor searching
Journal of the ACM (JACM)
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
An improved algorithm finding nearest neighbor using Kd-trees
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
ACM Transactions on Database Systems (TODS)
Similarity search and locality sensitive hashing using ternary content addressable memories
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Hausdorff distance under translation for points and balls
ACM Transactions on Algorithms (TALG)
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
An Optimal Randomized Cell Probe Lower Bound for Approximate Nearest Neighbor Searching
SIAM Journal on Computing
Approximate polytope membership queries
Proceedings of the forty-third annual ACM symposium on Theory of computing
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
Data-driven trajectory smoothing
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Approximate nearest neighbor search for low dimensional queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fully retroactive approximate range and nearest neighbor searching
ISAAC'11 Proceedings of the 22nd 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
Spherical lsh for approximate nearest neighbor search on unit hypersphere
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Approximate high-dimensional nearest neighbor queries using R-forests
Proceedings of the 17th International Database Engineering & Applications Symposium
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For a set P of n points in \mathbb{R}^d , we define a new type of space decomposition. The new diagram provides an \varepsilon-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d \geqslant 2. This contrasts with the standard Voronoi diagram that has \Omega (n^{\left\lceil {{d \mathord{\left/ {\vphantom {d 2}} \right. \kern-\nulldelimiterspace} 2}} \right\rceil } ) complexity in the worst case.