# Discrete Frechet distance for closed curves

arXiv: https://arxiv.org/abs/2106.02871 · HTML: https://mlsanity.com/paper/2106.02871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [Multiphysics discovery with moving boundaries using Ensemble SINDy and Peridynamic Differential Operator](https://mlsanity.com/paper/2303.15631/) (2023)
- [Beyond Chamfer Distance: Granular Order-aware Evaluation Metric For Online Mapping](https://mlsanity.com/paper/2605.22578/) (2026)

## Abstract (arXiv)

The paper presents a discrete variation of the Frechet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Frechet distance between two closed sequences of m and n points using binary search takes O(mn log mn) time. We present an algorithm that takes O(mn log* mn) time, where log* is the iterated logarithm.