Entropy-Bounded Computational Geometry Made Easier and Sensitive to Sortedness
Computational Geometry
2025-08-29 v1
Abstract
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and subsumes previous definitions of entropy used for sorting problems and structural entropy used in computational geometry. We provide simple algorithms for several problems, including 2D maxima, 2D and 3D convex hulls, and some visibility problems, and we show that they have running times depending on the range-partition entropy.
Keywords
Cite
@article{arxiv.2508.20489,
title = {Entropy-Bounded Computational Geometry Made Easier and Sensitive to Sortedness},
author = {David Eppstein and Michael T. Goodrich and Abraham M. Illickan and Claire A. To},
journal= {arXiv preprint arXiv:2508.20489},
year = {2025}
}
Comments
9 pages, 4 figures, appeared in CCCG 2025