Spurred by the surprising performance of recent implementations for the Fréchet distance, we perform algorithm engineering for the Fréchet distance under translation. Our solution combines fast, but inexact tools from continuous optimization (specifically, branch-and-bound algorithms for global Lipschitz optimization) with exact, but expensive algorithms from computational geometry (specifically, problem-specific algorithms based on an arrangement construction). We combine these two ingredients to obtain an exact decision algorithm for the Fréchet distance under translation. For the related task of computing the distance value up to a desired precision, we engineer and compare different methods. On a benchmark set involving handwritten characters and route trajectories, our implementation answers a typical query for either task in the range of a few milliseconds up to a second on standard desktop hardware.
We believe that our implementation will enable the use of the Fréchet distance under translation in applications, whereas previous approaches would have been computationally infeasible.