Abstract
We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases we give algorithms for finding a (1 + ε)-factor approximation of the Fréchet distance between two polygonal curves. We also consider the Fréchet distance between two polygonal curves among polyhedral obstacles in \(\mathcal{R}^3\) (1/ ∞ weighted region problem) and present a (1 + ε)-factor approximation algorithm.
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This work was supported in part by NSF award CCF-0635013.
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Cheung, Y.K., Daescu, O. (2009). Fréchet Distance Problems in Weighted Regions. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_12
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DOI: https://doi.org/10.1007/978-3-642-10631-6_12
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