Recognizing Weakly Simple Polygons

TL;DR

This paper introduces an efficient $O(n ext{log} n)$ algorithm for recognizing weakly simple polygons, significantly improving the previous $O(n^2 ext{log} n)$ approach, which is fundamental for various geometric algorithms.

Contribution

The paper presents the first $O(n ext{log} n)$ algorithm for recognizing weakly simple polygons, enhancing computational efficiency over prior methods.

Findings

The new algorithm runs in $O(n ext{log} n)$ time.

It improves recognition efficiency for weakly simple polygons.

The method is applicable to various geometric algorithms.

Abstract

We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input for several geometric algorithms. As such, how to recognize simple or weakly simple polygons is a fundamental question.