# How good is the Chord algorithm?

arXiv: https://arxiv.org/abs/1309.7084 · HTML: https://mlsanity.com/paper/1309.7084/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Ratio Covers of Convex Sets and Optimal Mixture Density Estimation](https://mlsanity.com/paper/2602.16142/) (2026)

## Abstract (arXiv)

The Chord algorithm is a popular, simple method for the succinct approximation of curves, which is widely used, under different names, in a variety of areas, such as, multiobjective and parametric optimization, computational geometry, and graphics. We analyze the performance of the Chord algorithm, as compared to the optimal approximation that achieves a desired accuracy with the minimum number of points. We prove sharp upper and lower bounds, both in the worst case and average case setting.