An O((log log n)2) Time Convex Hull Algorithm on Reconfigurable Meshes

It was open for more than eight years to obtain an algorithm for computing the convex hull of a set of n sorted points in sub-logarithmic time on a reconfigurable mesh of size p n pn. Our main contribution is to provide the first breakthrough: we propose an almost optimal algorithm running in O((log logn)2) time on a reconfigurable mesh of size p n pn. With slight modifications this algorithm can be implemented to run in O((log logn)2) time on a reconfigurable mesh of size p n log logn p n log logn . Clearly, the latter algorithm is work-optimal. We also show that any algorithm that computes the convex hull of a set of n sorted points on an n-processor reconfigurable mesh must take (log logn) time. Our result opens the door to efficient convex-hull-based algorithms on reconfigurable meshes.