ESA 2013: Algorithms – ESA 2013 pp 241-252 | Cite as
Computing the Fréchet Distance with a Retractable Leash
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 ℝ d 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.
Keywords
Euclidean Distance Line Segment Distance Function Cell Boundary Decision VersionPreview
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