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Four Soviets Walk the Dog: Improved Bounds for Computing the Fréchet Distance

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One popular measure is the Fréchet distance. Since it was proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original \(O(n^2 \log n)\) algorithm by Alt and Godau for computing the Fréchet...

Folding Free-Space Diagrams: Computing the Fr\'echet Distance between 1-Dimensional Curves (Multimedia Contribution)

By folding the free-space diagram for efficient preprocessing, we show that the Frechet distance between 1D curves can be computed in O(nk log n) time, assuming one curve has ply k.

Folding Free-Space Diagrams: Computing the Fr\'echet Distance between 1-Dimensional Curves (Multimedia Contribution)

By folding the free-space diagram for efficient preprocessing, we show that the Frechet distance between 1D curves can be computed in O(nk log n) time, assuming one curve has ply k.

Computing the Fréchet Distance with a Retractable Leash

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet...

Mapping Polygons to the Grid with Small Hausdorff and Fr\'echet Distance

, Technische Universiteit Eindhoven, 2014 . Wouter Meulemans . Discretized approaches to schematization . Computing Research Repository (arXiv) , abs/1606.06488 , 2016 . Emilio G. Ort?z-Garc?a , Sancho Salcedo

Mapping Polygons to the Grid with Small Hausdorff and Fr\'echet Distance

, Technische Universiteit Eindhoven, 2014 . Wouter Meulemans . Discretized approaches to schematization . Computing Research Repository (arXiv) , abs/1606.06488 , 2016 . Emilio G. Ort?z-Garc?a , Sancho Salcedo