We study the problem of how to breakup many point sets in Rd into smaller parts using a few splitting (shared) hyperplanes. This problem is related to the classical Ham-Sandwich Theorem. We provide a logarithmic approximation to the optimal solution using the greedy algorithm for submodular optimization.
@article{arxiv.1808.03260,
title = {Few Cuts Meet Many Point Sets},
author = {Sariel Har-Peled and Mitchell Jones},
journal= {arXiv preprint arXiv:1808.03260},
year = {2022}
}