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FOCS
1999
IEEE

Approximate Nearest Neighbor Algorithms for Hausdorff Metrics via Embeddings

9 years 4 months ago
Approximate Nearest Neighbor Algorithms for Hausdorff Metrics via Embeddings
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 recognitionand 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 l 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 l embedding.
Martin Farach-Colton, Piotr Indyk
Added 03 Aug 2010
Updated 03 Aug 2010
Type Conference
Year 1999
Where FOCS
Authors Martin Farach-Colton, Piotr Indyk
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