Algorithms for orthogonal partitioning into four parts
Combinatorics
2026-02-03 v2 Computational Geometry
Metric Geometry
Abstract
The famous pancake theorem states that for every finite set in the plane, there exist two orthogonal lines that divide into four equal parts. We propose an algorithm whose running time is linear in the number of points in and prove that this complexity is optimal. We also consider generalizations of the pancake theorem and show that orthogonal hyperplanes can be found in polynomial time.
Cite
@article{arxiv.2511.20866,
title = {Algorithms for orthogonal partitioning into four parts},
author = {Alexey Fakhrutdinov and Oleg R. Musin},
journal= {arXiv preprint arXiv:2511.20866},
year = {2026}
}