An optimal speed-up parallel algorithm for triangulating simplicial point sets in space

Previous research on developing parallel triangulation algorithms concentrated on triangulating planar point sets.O(log³ n) running time algorithms usingO(n) processors have been developed in Refs. 1 and 2. Atallah and Goodrich⁽³⁾ presented a data structure that can be viewed as a parallel analogue of the sequential plane-sweeping paradigm, which can be used to triangulate a planar point set inO(logn loglogn) time usingO(n) processors. Recently Merks⁽⁴⁾ described an algorithm for triangulating point sets which runs inO(logn) time usingO(n) processors, and is thus optimal. In this paper we develop a parallel algorithm for triangulating simplicial point sets in arbitrary dimensions based on the idea of the sequential algorithm presented in Ref. 5. The algorithm runs inO(log² n) time usingO(n/logn) processors. The algorithm hasO(n logn) as the product of the running time and the number of processors; i.e., an optimal speed-up.