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New Software and Platforms
New Results
Bibliography
New Software and Platforms
New Results
Bibliography


Section: New Results

Products of Euclidean Metrics and Applications to Proximity Questions among Curves

Participants : Ioannis Emiris, Ioannis Psarros.

In [18], we study Approximate Nearest Neighbor (ANN) search on 1-dimensional shapes. We start with distance functions between discretized curves in Euclidean space: they appear in a wide range of applications, from road segments and molecular backbones to time-series in general dimension. For p-products of Euclidean metrics, for any positive integer p, we design simple and efficient data structures for ANN, based on randomized projections, which are of independent interest. They serve to solve proximity problems under a notion of distance between discretized curves, which generalizes both discrete Fréchet and Dynamic Time Warping distances. These are the most popular and practical approaches to comparing such curves. We offer the first data structures and query algorithms for ANN with arbitrarily good approximation factor, at the expense of increasing space usage and preprocessing time over existing methods. Query time complexity is comparable or significantly improved by our algorithms.