In this paper we present an efficient parallel algorithm for polygon triangulation. The
algorithm we present runs in O (log n) time using O (n) processors, which is optimal if the
polygon is allowed to contain holes. This improves the previous parallel complexity bounds
for this problem by a log n factor. If we are also given a trapezoidal decomposition of the
polygon as input, then we can triangulate the polygon in O (log n) time using only O (n log n)
processors. This immediately implies that we can triangulate a monotone polygon in O (log …