Improved Algorithms for Partial Curve Matching
Back in 1995, Alt and Godau gave an efficient algorithm for deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm log(nm)), for n and m being the number of segments in the two curves, respectively. We improve this long-standing result by presenting an algorithm that solves this decision problem in O(nm) time. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fréchet distance problem, including the Fréchet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the case when the map is a directed acyclic graph.
KeywordsDirected Acyclic Graph Query Point Improve Algorithm Partial Curve Maximum Walk
Unable to display preview. Download preview PDF.
- 5.Buchin, K., Buchin, M., Knauer, C., Rote, G., Wenk, C.: How difficult is it to walk the dog? In: Proc. 23rd EWCG, pp. 170–173 (2007)Google Scholar
- 6.Buchin, K., Buchin, M., Wang, Y.: Exact algorithms for partial curve matching via the Fréchet distance. In: Proc. 20th ACM-SIAM Sympos. Discrete Algorithms, pp. 645–654 (2009)Google Scholar
- 7.Cook, A.F., Wenk, C.: Geodesic Fréchet distance inside a simple polygon. In: Proc. 25th Sympos. Theoret. Aspects Comput. Sci. LNCS, vol. 5664, pp. 193–204 (2008)Google Scholar
- 11.Maheshwari, A., Sack, J.-R., Shahbaz, K., Zarrabi-Zadeh, H.: Staying close to a curve. In: Proc. 23rd Canad. Conf. Computat. Geom. (to appear, 2011) Google Scholar
- 12.Sriraghavendra, E., Karthik, K., Bhattacharyya, C.: Fréchet distance based approach for searching online handwritten documents. In: Proc. 9th Internat. Conf. Document Anal. Recognition, pp. 461–465 (2007)Google Scholar