Abstract
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.
Research supported by NSERC, HPCVL, and SUN Microsystems.
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Maheshwari, A., Sack, JR., Shahbaz, K., Zarrabi-Zadeh, H. (2011). Improved Algorithms for Partial Curve Matching. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_44
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DOI: https://doi.org/10.1007/978-3-642-23719-5_44
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