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Approximability of the Discrete Fr\'echet Distance

S o C G ' Approximability of the Discrete Fréchet Distance Karl Bringmann 0 Wolfgang Mulzer 0 0 Institute of Theoretical Computer Science, ETH Zurich, Switzerland Institut für Informatik, Freie ... matching conditional lower bounds . arXiv:1408.1340 , 2014 . Kevin Buchin , Maike Buchin, Wouter Meulemans, and Wolfgang Mulzer . Four soviets walk the dog - with an application to Alt's conjecture . In Proc

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...

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...

Preprocessing Imprecise Points for Delaunay Triangulation: Simplified and Extended

Suppose we want to compute the Delaunay triangulation of a set P whose points are restricted to a collection ℛ of input regions known in advance. Building on recent work by Löffler and Snoeyink, we show how to leverage our knowledge of ℛ for faster Delaunay computation. Our approach needs no fancy machinery and optimally handles a wide variety of inputs, e.g., overlapping disks...

Stabbing Pairwise Intersecting Disks by Five Points

Wolfgang Mulzer 2 Institut für Informatik, Freie Universität Berlin , 14195 Berlin, Germany 3 Haim Kaplan School of Computer Science, Tel Aviv University , Tel Aviv