Given a point set S and a polygonal curve P in Rd, we study the problem of finding a polygonal curve through S, which has minimum Fréchet distance to P. We present an efficient algorithm to solve the decision version of this problem in O(nk2) time, where n and k represent the sizes of P and S, respectively. A curve minimizing the Fréchet distance can be computed in O(nk2 log(nk)) time. As a by-product, we improve the map matching algorithm of Alt et al. by an O(log k) factor for the case when the map is a complete graph.

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Conference 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
Citation
Maheshwari, A, Sack, J.-R, Shahbaz, K. (Kaveh), & Zarrabi-Zadeh, H. (Hamid). (2011). Staying close to a curve. In Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011.