Abstract
All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; then they use this oracle to find the optimum among a finite set of critical values. We present a novel approach that avoids the detour through the decision version. We demonstrate its strength by presenting a quadratic time algorithm for the Fréchet distance between polygonal curves in ℝd under polyhedral distance functions, including L 1 and L ∞ . We also get a (1 + ε)-approximation of the Fréchet distance under the Euclidean metric. For the exact Euclidean case, our framework currently gives an algorithm with running time O(n 2 log2 n). However, we conjecture that it may eventually lead to a faster exact algorithm.
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Buchin, K., Buchin, M., van Leusden, R., Meulemans, W., Mulzer, W. (2013). Computing the Fréchet Distance with a Retractable Leash. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_21
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DOI: https://doi.org/10.1007/978-3-642-40450-4_21
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