Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Matching shapes with a reference point
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
RAPID: randomized pharmacophore identification for drug design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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
Improved algorithms for robust point pattern matching and applications to image registration
Proceedings of the fourteenth annual symposium on Computational geometry
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Geometric Manipulation of Flexible Ligands
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Pattern Matching for Spatial Point Sets
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On Approximate Nearest Neighbors in Non-Euclidean Spaces
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Approximate nearest neighbors and sequence comparison with block operations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximate nearest neighbor algorithms for Frechet distance via product metrics
Proceedings of the eighteenth annual symposium on Computational geometry
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Pattern Recognition Letters
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Structural risk minimization using nearest neighbor rule
ICME '03 Proceedings of the 2003 International Conference on Multimedia and Expo - Volume 2
Communications of the ACM
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Hausdorff metrics are used in geometric settings for measuring the distance between sets of points. They have been used extensively in areas such as computer vision, pattern recognition and computational chemistry.While computing the distance between a single pair of sets under the Hausdorff metric has been well studied, no results were known for the Nearest Neighbor problem under Hausdorff metrics. Indeed, no results were known for the nearest neighbor problem for any metric without norm structure, of which the Hausdorff is one.We present the first nearest neighbor algorithm for the Hausdorff metric. We achieve our result by embedding Hausdorff metrics into l1 and using known nearest neighbor algorithms for this target metric. We give upper and lower bounds on the number of dimensions needed for such an l1 embedding. Our bounds require the introduction of new techniques based on superimposed codes and non-uniform sampling.