Abstract
The similarity of two polygonal curves can be measured using the Fréchet distance. We introduce the notion of a more robust Fréchet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural approach for handling noise, in particular batched outliers. We compute a constant factor approximation to the minimum Fréchet distance over all possible such shortcuts. Our algorithm runs in O(c^2 kn log^3 n) time if one is allowed to take at most k shortcuts and the input curves are c-packed. For the case where the number of shortcuts is unrestricted, we describe an algorithm which runs in O(c^2 n log^3 n) time. To facilitate the new algorithm we develop several new data-structures, which we believe to be of independent interest: (i) for range reporting on a curve, and (ii) for preprocessing a curve to answer queries for the Fréchet distance between a subcurve and a line segment.
Original language | English |
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Title of host publication | Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'12),17-19 january 2012, Kyoto, Japan |
Editors | Y. Rabani |
Publisher | Society for Industrial and Applied Mathematics (SIAM) |
Pages | 318-327 |
ISBN (Print) | 978-1-61197-210-8 |
DOIs | |
Publication status | Published - 2012 |
Externally published | Yes |
Event | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012) - Westin Miyako, Kyoto, Japan Duration: 17 Jan 2012 → 19 Jan 2012 Conference number: 23 http://www.siam.org/meetings/da12/ |
Conference
Conference | 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012) |
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Abbreviated title | SODA '12 |
Country | Japan |
City | Kyoto |
Period | 17/01/12 → 19/01/12 |
Internet address |