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

@article{Buchin2017FourSW,
  title={Four Soviets Walk the Dog: Improved Bounds for Computing the Fr{\'e}chet Distance},
  author={Kevin Buchin and Maike Buchin and Wouter Meulemans and Wolfgang Mulzer},
  journal={Discrete \& Computational Geometry},
  year={2017},
  volume={58},
  pages={180-216}
}
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 $$O(n^2 \log n)$$O(n2logn) algorithm by Alt and Godau for computing the Fréchet distance remains the state of the art (here, n denotes the number of edges on each curve). This has led Helmut… 

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