# Entropy-Bounded Computational Geometry Made Easier and Sensitive to Sortedness

## TL;DR

This paper introduces a new entropy measure called range-partition entropy for computational geometry, providing simple algorithms for various problems with running times dependent on this measure.

## Contribution

It unifies previous entropy measures in computational geometry and offers new algorithms with entropy-dependent running times.

## Key findings

- Algorithms for 2D maxima, convex hulls, and visibility problems
- Running times depend on the new range-partition entropy
- Simplifies and improves understanding of entropy-bounded geometric algorithms

## 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.