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 pn pn. Our main contribution is to provide the first breakthrough: we propose an almost optimal algorithm running in Ologlog n2 time on a reconfigurable mesh of size pn pn. With slight modifications this algorithm can be implemented to run in Ologlog n2 time on a reconfigurable mesh of size pn log log n pn log log n. 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 log ntime. Our result opens the door to efficient convex-hull-based algorithms on reconfigurable meshes.

• Type: Conference
• Year: 1998
• Where: IPPS
• Authors: Tatsuya Hayashi, Koji Nakano, Stephan Olariu
• Keywords: Algorithms, Distributed And Parallel Computing, IPPS 1998, Reconfigurable Mesh, Size Pn