Time-optimal sorting and applications on n*n enhanced meshes

Time-optimal sorting and convex hull algorithms are proposed for two classes of enhanced meshes, the mesh with multiple broadcasting and the reconfigurable mesh. The authors show that the fundamental problem of sorting n items can be solved in O(log n) time on a mesh with multiple broadcasting of size n*n, which leads to an O(log n) time algorithm to compute the convex hull of an arbitrary set of n points in the plane. Based on the constant-time sorting algorithm on reconfigurable meshes, it is suggested that the convex hull problem of size n can be solved in constant time on a reconfigurable mesh of size n*n. All these algorithms can achieve time lower bounds for their respective models of computation.<>