Defines rock climber and k-station distances for polygonal chains with alternating agent moves, proves equivalence to Fréchet or Hausdorff for unlimited moves, shows NP-hardness for fixed k, and gives a 2-approximation for the minimum k achieving a distance threshold.
Four Sovi- ets walk the dog: Improved bounds for computing the Fr´ echet distance
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The paper delivers a chronological history of Fréchet distances connecting early abstract set theory to curve metrics, optimal transport, and the FID metric in generative models.
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Rock Climber Distance: Frogs versus Dogs
Defines rock climber and k-station distances for polygonal chains with alternating agent moves, proves equivalence to Fréchet or Hausdorff for unlimited moves, shows NP-hardness for fixed k, and gives a 2-approximation for the minimum k achieving a distance threshold.
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A Brief History of Fr\'echet Distances: From Curves and Probability Laws to FID
The paper delivers a chronological history of Fréchet distances connecting early abstract set theory to curve metrics, optimal transport, and the FID metric in generative models.