Time- and VLSI-optimal convex hull computation on meshes with multiple broadcasting

Our main contribution is to present the first known general-case, time- and VLSI-optimal, algorithm for convex hull computation on meshes with multiple broadcasting. Specifically, we show that for every choice of a positive constant ε, the convex hull of a set of an arbitrary set of m (n 1 2 + ε ⩽ m ⩽ n) points in the plane input in the first ⌉ m √n ⌈ columns of a mesh with multiple broadcasting of size √ n × √ n can be computed in Θ ( m √n ) time.