# Folding a Paper Strip to Minimize Thickness

arXiv: https://arxiv.org/abs/1411.6371 · HTML: https://mlsanity.com/paper/1411.6371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2014.

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

- [COrigami: An AI Pipeline for Co-Designing Flat-Foldable Visually Recognisable Origami](https://mlsanity.com/paper/2606.26299/) (2026)

## Abstract (arXiv)

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a "flat folding" is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where "thicker" creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.