Edge Flip algorithm is proposed by Charles Lawson in 1972. Details of the algorithm is discused in [5]. A three dimensional interpretation of triangulations and of Edge Flip algorithm (given in the same paper [5]) concludes that an edge is subject to flip operation at most once. Since there are at most 
edges of a graph with n vertices, there are fewer than 
edge flip operations. Hence it takes 
time to construct Delaunay Triangulation, starting from an arbitrary triangulation. Since we can construct a triangulation in 
time using plane sweep, it takes 
time to construct Delaunay Triangulation of a set of points S of size n.