Randomized algorithms
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth 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
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
A note on the nearest neighbor in growth-restricted metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Disorder inequality: a combinatorial approach to nearest neighbor search
WSDM '08 Proceedings of the 2008 International Conference on Web Search and Data Mining
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
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
Indexability, concentration, and VC theory
Proceedings of the Third International Conference on SImilarity Search and APplications
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
Indexability, concentration, and VC theory
Journal of Discrete Algorithms
Approximate bregman near neighbors in sublinear time: beyond the triangle inequality
Proceedings of the twenty-eighth annual symposium on Computational geometry
| Hi-index | 0.00 |
We define a natural notion of efficiency for approximate nearest-neighbor (ANN) search in general n-point metric spaces, namely the existence of a randomized algorithm which answers (1 + ε)-ANN queries in polylog(n) time using only polynomial space. We then study which families of metric spaces admit efficient ANN schemes in the black-box model, where only oracle access to the distance function is given, and any query consistent with the triangle inequality may be asked.For ε Rn, Bull. Soc. Math. France 111 (4) (1983) 429-448]), we show that a metric space X admits an efficient (1+ε)-ANN scheme for any ε X) = O(log log n). For coarser approximations, clearly the upper bound continues to hold, but there is a threshold at which our lower bound breaks down--this is precisely when points in the "ambient space" may begin to affect the complexity of "hard" subspaces S ⊆ X. Indeed, we give examples which show that dim(X) does not characterize the black-box complexity of ANN above the threshold.Our scheme for ANN in low-dimensional metric spaces is the first to yield efficient algorithms without relying on any additional assumptions on the input. In previous approaches (e.g., [K.L. Clarkson, Nearest neighbor queries in metric spaces, Discrete Comput. Geom. 22(1) (1999) 63-93; D. Karger, M. Ruhl, Finding nearest neighbors in growth-restricted metrics, in: 34th Annu. ACM Symp. on the Theory of Computing, 2002, pp. 63-66; R. Krauthgamer, J.R. Lee, Navigating nets: simple algorithms for proximity search, in: 15th Annu. ACM-SIAM Symp. on Discrete Algorithms, 2004, pp. 791-801; K. Hildrum, et al., A note on finding nearest neighbors in growth-restricted metrics, in: Proc. of the 15th Annu. ACM-SIAM Symp. on Discrete Algorithms, 2004, pp. 560-561]), even spaces with dim(X) = O(1) sometimes required Ω(n) query times.