Why Walking the Dog Takes Time: Frechet Distance Has No Strongly Subquadratic Algorithms Unless SETH Fails

  title={Why Walking the Dog Takes Time: Frechet Distance Has No Strongly Subquadratic Algorithms Unless SETH Fails},
  author={Karl Bringmann},
  journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
  • K. Bringmann
  • Published 5 April 2014
  • Computer Science, Mathematics
  • 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
The Fréchet distance is a well-studied and very popular measure of similarity of two curves. Many variants and extensions have been studied since Alt and Godau introduced this measure to computational geometry in 1991. Their original algorithm to compute the Fréchet distance of two polygonal curves with n vertices has a runtime of O(n^2 log n). More than 20 years later, the state of the art algorithms for most variants still take time more than O(n2 / log n), but no matching lower bounds are… 

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