Recognizing Weakly Simple Polygons

We present an O(nlog n) -time algorithm that determines whether a given n -gon in the plane is weakly simple. This improves upon an O(n^2log n) -time algorithm by Chang et al. (Proceedings of the 26th ACM-SIAM symposium on discrete algorithm, SIAM, 2015 ). Weakly simple polygons are required as input for several geometric algorithms. As such, recognizing simple or weakly simple polygons is a fundamental problem.