Computational geometry: an introduction
Computational geometry: an introduction
Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
Constant-time convexity problems on reconfigurable meshes
Journal of Parallel and Distributed Computing
Constant Time Algorithms for Computational Geometry on the Reconfigurable Mesh
IEEE Transactions on Parallel and Distributed Systems
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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 驴n 脳 驴n. Our main contribution is to provide the first breakthrough: we propose an almost optimal algorithm running in O((log log n)2) time on a reconfigurable mesh of size 驴n 脳 驴n. With slight modifications this algorithm can be implemented to run in O((log log n)2) time on a reconfigurable mesh of size 驴n/log log n 脳 驴n/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 驴(log log n) time. Our result opens the door to efficient convex-hull-based algorithms on reconfigurable meshes.