AN O(n log log n)-TIME ALGORITHM FOR TRIANGULATING A SIMPLE POLYGON
Robert E. Tarjan
Christopher J. Van Wyk
Given a simple n-vertex polygon, the triangulation problem is to partition the interior of the polygon into n-2 triangles by adding n-3 nonintersecting diagonals. We propose an O(n log logn)-time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangulation is not as hard as sorting. Improved algorithms for several other computational geometry problems, including testing whether a polygon is simple, follow from our result.